Wiener Index Research Papers - Academia.edu (original) (raw)

Motivated by some recent research on the terminal (reduced) distance matrix, we consider the terminal Wiener index (T W ) of trees, equal to the sum of distances between all pairs of pendent vertices. A simple formula for computing T W is... more

- by
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- Computing, Mathematical Sciences, Tree, Mathematical chemistry

The generalization of ecological results from temporary streams needs the study of those ecosystems across a broad scale of running waters, covering the geographical ecological constraints involved (e.g., precipitation, temperature and geology). For the particular situation of Mediterranean streams in Southern Europe, high changes in water level, with unpredicting flood events, represent an important factor determining the structure and function of Mediterranean streams. This variability, inducing accentuated changes in the macroinvertebrate community, tends to influence the assessment methodologies. A set of metrics commonly used in Europe to assess organic degradation (Shannon-Wiener index, evenness, richness, BBI, IBE, BMWP , ASPT , DSFI, EPT, number of Trichoptera families, percentage of Gasteropoda, Oligochaeta and Diptera) and a multimetric index (IM9) developed to assess organic degradation in southern siliceous Portuguese basins were tested to evaluate quality at two contrasting sites (one unimpaired and another impaired by an identified point source of pollution). The multimetric index (IM9) composed by: ASPT (average score per taxon); GOLD (one minus percentage of Gasteropoda, Oligochaeta and Diptera); and TRICF (number of Trichoptera families), was the most suitable assessment methodology. IM9 presented a quite stable temporal pattern from February in late winter until June in early summer, even under the effect of episodic floods. A stepwise regression showed that most of tested metrics were significantly related to environmental variables (soluble reactive phosphorous, dissolved inorganic nitrogen and dissolved oxygen). Only richness, IBE and BMWP were not significantly influenced by environmental variables. Future research must be done covering the complete gradient of organic degradation, including the extension of multimetric assessment methodologies to temporary streams located in other regions under different geological and climatic conditions.

- by Manuela Morais
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- Earth Sciences, Water quality, Biological Sciences, Protein Structure and Function

The generalization of ecological results from temporary streams needs the study of those ecosystems across a broad scale of running waters, covering the geographical ecological constraints involved (e.g., precipitation, temperature and geology). For the particular situation of Mediterranean streams in Southern Europe, high changes in water level, with unpredicting flood events, represent an important factor determining the structure and function of Mediterranean streams. This variability, inducing accentuated changes in the macroinvertebrate community, tends to influence the assessment methodologies. A set of metrics commonly used in Europe to assess organic degradation (Shannon–Wiener index, evenness, richness, BBI, IBE, BMWP′, ASPT′, DSFI, EPT, number of Trichoptera families, percentage of Gasteropoda, Oligochaeta and Diptera) and a multimetric index (IM9) developed to assess organic degradation in southern siliceous Portuguese basins were tested to evaluate quality at two contrasting sites (one unimpaired and another impaired by an identified point source of pollution). The multimetric index (IM9) composed by: ASPT′ (average score per taxon); GOLD (one minus percentage of Gasteropoda, Oligochaeta and Diptera); and TRICF (number of Trichoptera families), was the most suitable assessment methodology. IM9 presented a quite stable temporal pattern from February in late winter until June in early summer, even under the effect of episodic floods. A stepwise regression showed that most of tested metrics were significantly related to environmental variables (soluble reactive phosphorous, dissolved inorganic nitrogen and dissolved oxygen). Only richness, IBE and BMWP′ were not significantly influenced by environmental variables. Future research must be done covering the complete gradient of organic degradation, including the extension of multimetric assessment methodologies to temporary streams located in other regions under different geological and climatic conditions.

This paper provides a botanical inventory of a forest community in the North Negros Forest Reserve that is disproportionately valuable from a conservation perspective. The forest fragment is one of the last remaining wet tropical rainforest ecosystems in the biogeographic region of the West Visayas and an important refuge for a large number of endemic species. Using standard methods of the Philippine Plant Inventory Project we described the structure and composition of this little known forest type in the transition zone between lowland and lower montane forest. A 1 ha inventory plot 500 × 20 m in size was established and all trees of 10 cm DBH or greater were measured and permanently labeled. Subsequently, fertile specimens were collected over a period of 18 months. We found 645 individuals belonging to 92 species, 54 genera and 39 families with a combined basal area of 58.8 m 2 and an average canopy height of 30 m. This community was not dominated by dipterocarps. Species of Lauraceae, Burseraceae, Sapotaceae and Icainaceae were equally or more important. Diversity measured as Shannon-Wiener index (5.59), equitability index (0.86) and Simpson index (0.032) was high, and no single family or species dominated the plot.

- by E. Curio
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- Ecology, Biodiversity Conservation, Mantle Transition Zone, Endemic species

- by Andrey Dobrynin
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- Applied Mathematics, Communication Theory, Eigenvalues, Super Line Graph

Th is review addresses the intersection of water quality policy and benthic macroinvertebrates. Specifi cally, we examine the role that stream macroinvertebrates have played or could play in informing water quality decisions given the current policy framework, using this framework as the organizational structure for the review. Macroinvertebrates, as biological indicators of stream water quality, can be utilized to identify impaired waters, determine aquatic life stressors, set pollutant load reductions, and indicate improvement. We present both current approaches as well as innovative approaches to identify macroinvertebrates and aquatic life stressors. We also discuss an example of the environmental management approach, specifi cally, how macroinvertebrates can be used to indicate the relative success of stream restoration. For policymakers, this review serves to illuminate opportunities and limitations of using benthic macroinvertebrates as indicators of water quality. For entomologists, this review highlights policy-relevant research questions that would further aid the classifi cation of impaired waters, the identifi cation of stressors, or the management of stream ecosystems.

- by Ariana Sutton-grier
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- Water quality, Ecology, Transylvanian Romanians, River Basin
- by Baoquan Li
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- Community Structure, Species Richness, Primary Production, Human Activity

Molecular graph serves as a convenient model for any real or abstract chemical compound. A topological index is the graph invariant number calculated from the graph representing the molecule. The advantage of topological indices is that it may be used directly as simple numerical descriptors in QSPR/QSAR models. Most of the topological descriptors are based either on atom-atom connectivity or on topological distances. A chemical reaction can be represented as the transformation of the chemical (Molecular) graph representing the reaction's substrate into another chemical graph representing the product. The type of chemical reaction where two substrates combine to form a single product (combination reaction) motivated us to study the effect of topological indices when a bridge is introduced between the respective vertices (of degree i, i=1, 2, 3) of two copies of the same graph. The graph obtained in this manner may or may not exist in reality, but it is the interest of the chemist to check the stability of the so obtained structure of the product. In this paper we present an algorithm to calculate the distance matrix of the resultant graph obtained after each iteration and thereby tabulate various topological indices. We also give the explicit formula for calculating Wiener index of the graph representing the resulting product.

- by iir publications
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- Mathematics, Graph Theory, Graph, Molecules

Recent Ostracoda assemblages of the Caicedo de Yuso Lake have been described as representative of palustrine/ lacustrine environments in Iberian temperate lakes. This study considers the changes in assemblages at a fixed station during two consecutive annual cycles, as well as their distribution in summer and winter profiles of the lake. Total sampleassemblages have been quantified as species diversities, measured by the Shannon-Wiener index H (S). The trends of this index are compared to physical parameters (temperature, conductivity, dissolved oxygen, CO 2 ) of the bottom waters of this lake. The Ostracoda assemblages (8100 adults and juvenile living specimens, belonging to 20 species) are dominated by Cypria ophtalmica, Cypridopsis vidua and Pseudocandona marchica. Biocenotic assemblages are well developed in the western, flat shelf area of the lake (0 to 9 m in depth), where a major substrate of charophytes permits assemblages with moderate diversity levels to be maintained. Waters below 10 m are practically barren of living individuals, and only few specimens of the generalist species Cypria ophtalmica have been found alive at that depth. Differential responses of most abundant species to changes in the environmental parameters of the bottom of the lake have been interpreted in terms of the ecological requirements of those species. Most of these responses are clearly influenced by shifts in the parameters mentioned, and decreases in oxygen and increases in CO 2 produce particularly marked falls in assemblage diversity levels. Conversely, when the oxygen increases and the CO 2 falls, the diversity levels increase. The time delay in responding to these changes is estimated at less than one month. This general behaviour of the ostracod assemblages of Caicedo Lake is not followed by C. ophtalmica, which is considered a particular species that can stand hypoxic waters, with relatively high CO 2 concentrations. This ability of C. ophtalmica allows specimens of this species to occupy deep and environmentally unfavourable niches in the lake, that no other ostracod species of Caicedo Lake does. The knowledge of areal and temporal distribution of Ostracoda species in a temperate lake, such as Caicedo de Yuso, exhibits a good potential for 0031-0182/$ -see front matter D (J. Rodriguez-Lazaro).

- by Maite Martin-rubio and +2
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- Evolutionary Biology, Geology, Ecology, Time Delay

The aqueous solubility (S w ) of liquids and solids, expressed as log S w as well as their partition coefficients in different solvent systems viz. P oct (partition coefficient in octanol-water), P 16 (partition coefficient in water-hexadecane), P alk (partition coefficient in water-alkane), and P cyc (partition coefficient in water-cyclohexane), and aqueous solubility (S w ) have been estimated using the PI (Padmakar-Ivan) index and the results compared with those obtained using the widely used Wiener index (W). Regression analysis of the data using n-alkanes show that the PI index gives better results than the W index. #

- by Dheeraj Mandloi
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- Algorithms, Organic Chemistry, Physical Chemistry, Water

Patterns of woody regeneration in terms of species composition and diversity were studied in a 37-year-old teak plantation established on degraded mixed deciduous forest (MDF) at Mae Yuak Plantation Station, Ngao District, Lampang Province, Northern Thailand. In order to assess the role of plantations in regeneration of woody tree species within the plantation, the understorey floristic structures and composition were evaluated fifteen 20 m Â 20 m plots at three sites differing in topographic position, stand structure and distance from natural forest. The average density and species richness of woody regeneration in the plantation was 556.7 stem ha À1 and 9.6 species plot À1 , respectively. The Shannon-Wiener index was 2.47-2.68, and Sorensen's index of similarity between plantation and the adjacent MDF was 0.38-0.55. A total of 334 woody regeneration individuals were found in 0.6 ha of teak plantation, representing 37 species, with Leguminosae the most common family. Pterocarpus macrocarpus Kurz (Leguminosae) showed the highest density of 73.3 stem ha À1 . The eight most dominant species were P. macrocarpus, Dalbergia oliveri Gamble, Croton roxburghii N.P. Balakr, Xylia xylocarpa (Roxb.) Tuab., D. cultrate Graham ex Benth., Wrightia arborea (Dennst.) Mabb., Schleichera oleosa (Lour.) Oken and Morinda tomentosa Heyne ex Roth. The proximity to the natural forest, seed dispersal characteristics and site qualities influenced woody regeneration. These results show teak plantations could be effective tools in rehabilitating degraded MDF in Northern Thailand. #

Home gardens are important for enhancing food and nutritional security for

- by Paul Struik
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- Statistical Significance, Cross Section, Plant species, Interaction effect

The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. The paper outlines the results known for W of trees: methods for computation of W and combinatorial expressions for W for various classes of trees, the isomorphism-discriminating power of W , connections between W and the center and centroid of a tree, as well as between W and the Laplacian eigenvalues, results on the Wiener indices of the line graphs of trees, on trees extremal w.r.t. W , and on integers which cannot be Wiener indices of trees. A few conjectures and open problems are mentioned, as well as the applications of W in chemistry, communication theory and elsewhere. : Primary 05C12, 05C05; Secondary 05C90.

- by Andrey Dobrynin
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- Applied Mathematics, Communication Theory, Eigenvalues, Super Line Graph

The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the elementary properties of this polynomial and compute it for some common graphs. We then find a formula for the Wiener polynomial of a dendrimer, a certain highly regular tree of interest to chemists, and show that it is unimodal. Finally, we point out a connection with the Poincaré polynomial of a finite Coxeter group.

- by Sumeet Gairola
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- Altitudinal gradient, Species Richness, Oak, Indian science

Chemical structures of organic compounds are characterized numerically by a variety of structural descriptors, one of the earliest and most widely used being the Wiener index W, derived from the interatomic distances in a molecular graph. Extensive use of such structural descriptors or topological indices has been made in drug design, screening of chemical databases, and similarity and diversity assessment. A new set of topological indices is introduced representing a partitioning of the Wiener index based on counts of even and odd molecular graph distances. These new indices are further generalized by weighting exponents which can be optimized during the quantitative structure-activity/-property relationship (QSAR/QSPR) modeling process.

- by William Seitz and +1
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- Chemical, Drug Design, Refractive Index, Heat Capacity

A unified approach to the Wiener topological index and its various recent modifications, is presented. Among these modifications particular attention is paid to the Kirchhoff, Harary, Szeged, Cluj and Schultz indices, as well as their numerous variants and generalizations. Relations between these indices are established and methods for their computation described. Correlation of these topological indices with physico-chemical properties of molecules, as well as their mutual correlation are examined.

- by Z. Tomovic and +2
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- Wiener Index, Topological Indices

The aim of this work was to study the effect of long-term contrasting cropping systems on the indigenous arbuscular mycorrhizal fungal (AMF) spore populations in the soil of a field experiment located in western Finland. Conventional and low-input cropping systems were compared, each with two nutrient management regimes. The conventional cropping system with a nonleguminous 6-year crop rotation (barley-barley-rye-oatpotato-oat) was fertilized at either full (rotation A) or half (rotation B) the recommended rate. In the low-input cropping system, plant residues were returned to the plots either as such (rotation C) or composted (rotation D). In the rotation of this system, 1 year with barley was replaced by clover, and oat was cultivated mixed with pea. Thus, the 6-year rotation was barley-red cloverrye-oat + pea-potato-oat + pea. Each rotation was replicated three times, starting the 6-year rotation in three different years, these being designated point 1, point 2, and point 3, respectively. In the low-input system, biotite and rock phosphate were used to compensate for K and P in the harvested yield, while animal manure was applied at the start only. After 13 years, rotation points 1 and 3 were studied. Barley was the standing crop in all plots of rotation point 1, while oat and oat + pea were grown in rotations C and D, respectively. AMF spores were studied by direct extraction and by trapping, sampled on 15 June and 15 August. In addition, a special assay was designed for isolation of fast colonizing, dominating AMF. The cropping system did not significantly affect AMF spore densities, although the low-input cropping system with composted plant residues had the highest density with 44 spores on average and the conventional system with full fertilization 24 spores per 100 cm 3 soil in the autumn samples. Species richness was low in the experimental area. Five Glomus spp., one Acaulospora, and one Scutellospora were identified at the species level. In addition to these, three unidentified Glomus spp. were found. Species richness was not affected by cropping system, rotation point, or their interactions. The Shannon-Wiener index of AMF spore distributions was significantly higher in the fully fertilized than in the half-fertilized conventional plots. Glomus claroideum was the most commonly identified single species in the experimental area. It occurred in all the cropping systems and their various rotation points, representing about 30% of the total number of identified spores. In August, G. claroideum accounted for as much as 45-55% of the total numbers of spores identified in the conventional system with halved fertilization. In contrast, Glomus mosseae occurred more commonly in June (26%) than in August (9%). A bioassay using roots as inoculum for isolation and culture of dominating AMF was successfully developed and yielded only G. claroideum. This indicates a high probability of being able to more generally identify, isolate, and culture fast colonizing generalist AMF for use as inoculants in agriculture and horticulture.

- by Helena Kahiluoto
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- Microbiology, Soil, Plant Biology, Agriculture

The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. Hexagonal systems (HS's) are a special type of plane graphs in which all faces are bounded by hexagons. These provide a graph representation of benzenoid hydrocarbons and thus find applications in chemistry. The paper outlines the results known for W of the

- by Andrey Dobrynin
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- Applied Mathematics, Graph Representation, Wiener Index

In this research, we give a GAP program for computing the Wiener and the Schultz indices of any graph. In addition, we compute the Wiener and the Schultz of HAC 5 C 7 [p, q] nanotube by this program.

- by Ali Iranmanesh and +1
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- Multidisciplinary, Indexation, Wiener Index

Patterns of plant and animal diversity were studied in a 10-year-old native species reforestation area at a bauxite-mined site at Porto Trombetas in western Pará State, Brazil. Understorey and overstorey floristic composition and structure, understorey light conditions, forest floor development and soil properties were evaluated in a total of 38 78.5-m 2 plots located in the reforestation area at varying distances up to 640 m from the boundary with the surrounding primary forest. Wildlife surveys focusing primarily on birds and bats were also conducted to assess the role of seed-dispersing animals in regeneration of woody forest species within the plantations and colonization by primary forest species not included in the original reforestation. Regeneration density, species richness and species diversity (Shannon-Wiener index) for woody perennial species, vines, herbs and grasses were strongly correlated with the diversity of planted tree species and structural development parameters, degree of forest floor development and soil pH. The better developed closed-canopy plots (Ͼ40% crown closure) were characterized by relatively well-developed litter (O1) and humus (O2) layers, more acidic soils being typical of the surrounding primary forests, and a more diverse herb, vine and woody perennial flora with a greater representation of primary forest species being characteristic of late secondary forests. In closed-canopy plots a total of 125 tree, palm and shrub species were censused (versus 34 in the more open-canopy plots), of which 75 species are known to have been introduced by natural means from the surrounding primary forest (versus 11 species in the open-canopy plots). Among the plantation plots, there was significant colonization by primary forest woody species up to 640 m away from the primary forest edge, although both the abundance and the diversity of colonizing species declined with increasing distance into the plantations. Smaller-seeded primary forest woody species dispersed by mammals and birds represented a higher proportion of the colonizing species compared with the larger-seeded species. These data are consistent with the results of the wildlife surveys, which indicated that most animal seed dispersal is provided by bats, that the most common frugivorous bat and bird species in the plantations feed on small-seeded plant species and that birds and mammals that typically disperse larger-seeded tree species (such as toucans, trogons, tapirs, deer and primates) are still rare in the reforestation area. These results suggest that while the reforestation program has been successful in creating a favorable environment for regeneration of a native primary forest species, further management interventions, such as enrichment plantings, may be required to accelerate regeneration of largeseeded primary forest species. © 1997 Elsevier Science B.V.

The long-term Colônia record is located in the Atlantic rainforest domain in Brazil (23°52′S 46°42′20″W 900 m a.s.l.). The 780 cm long core CO3 provides a coverage of a complete interglacial/glacial cycle for the first time in a neotropical rainforest. Information on the behavior of tropical climates compared to global changes in temperatures indicates specific climate responses in terms of precipitation at these latitudes. Winter extratropical circulation was very active during the last interglacial and most of the glacial. Floristic composition of the rainforest changed several times in each phase of expansion, twice during the interglacial, and three times during glacial episodes. Araucaria was well developed in the area of São Paulo until the beginning of the first dry phase of the glacial at ca. 50,000 yr B.P. Changes in insolation controlled the expansion of the rainforest and the tropical hydrological cycle as evidenced by a strong precession signal. However precession had no impact on regional climatic features. The two interglacials (MIS 5e and Holocene) showed completely different patterns attesting to the continuous evolution of the forest. The biodiversity index (Shannon-Wiener Index) remained high during both the interglacial and glacial attesting to the permanence of small patches of rainforest refugia during drier phases. The lowest Shannon-Wiener Indexes were recorded between 23,000 and 12,000 yr B.P. and 40,000 and 30,000 yr B.P. and characterize two marked phases of stress for the rainforest.

- by Claudio Riccomini
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- Evolutionary Biology, Palaeogeography, Palaeoclimatology, Geology

A total of sixtynine foraminiferal species have been identified from the sediment samples collected from the Chilka Lake during November 1997 and March, May 1998. These species have been quantitatively studied in regard to their relative abundance and distribution. Frequency distribution study of Foraminifera shows that Miliammina fusca, Ammobaculites exiguus, Trochammina hadai, Jadammina macrescens, Gaudryina exilis, Ammonia beccarii (Linne), A.

- by K. Jayalakshmy
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- Seasonality, Species Diversity, Relative Abundance, Indexation

The Randić index R(G) of a graph G=(V,E) is the sum of (d(u)d(v))−1/2 over all edges uv∈E of G. Bollobás and Erdős (Ars Combin. 50 (1998) 225) proved that the Randić index of a graph of order n without isolated vertices is at least n−1.... more

- by Odile Favaron
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- Applied Mathematics, Pure Mathematics, Discrete Mathematics, Lower Bound
- by Wolfgang R. Schmidt
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- Forest Ecology And Management, Productivity, Biodiversity, Forest Ecology

The aim of this study was to estimate the influence of Ceratophyllum demersum L. and Stratiotes aloides L. on the species richness and phytocoenotic diversity of aquatic vegetation in lakes. The study was based on field investigations in the Łęczna-Włodawa Lake District located in mid-eastern Poland. The studied lakes (32) included both polymictic and dimictic reservoirs. Both in the polymictic and dimictic lakes, statistically significant correlation coefficients were obtained between the parameters that characterize Stratiotes aloides (the frequency in the phytosociological relevés, the percent share of Stratiotetum aloidis association in the phytolittoral) and those characteristic for species richness (the total number of hydromacrophytes, the number of charophytes, elodeids, nymphaeids and lemnids), phytocoenotic richness (the mean number of species in the phytosociological relevés) and phytocoenotic diversity (the Shannon-Wiener Index). The communities with a share of S. aloides are characterized by higher species richness. However, not a single case of statistically significant dependency was reported between the parameters that describe C. demersum (the frequency in the phytosociological relevés, the percent share Ceratophylletum demersi association in the phytolittoral) and the vegetation traits in both lake groups. Common occurrence of Stratiotes aloides might be considered to be evidence for good status of an aquatic ecosystem and a very good indicator of species richness and diversity of aquatic vegetation.

- by Stanisław Chmiel
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- Earth Sciences, Hydrobiology, Biological Sciences, Aquatic Ecosystem

The classical Wiener index, W(G), is equal to the sum of the distances between all pairs of vertexes of a (molecular) graph, G. We now consider a related topological index, π(G), equal to the product of distances between all pairs of vertexes of G. The basic properties of the π index are established and its possible physicochemical applications examined. In the case of alkanes, π and W are highly correlated; a slightly curvilinear correlation exists between ln π and W.

- by Z. Tomovic
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- THEORETICAL AND COMPUTATIONAL CHEMISTRY, Wiener Index

Let G=(V,E) be a graph where v(G) and E(G) are vertices and edges of G, respectively. Sum of distance between vertices of graphs is called wiener invariant. In This paper, we present some proved results on the wiener invariant and some... more

- by Soft Computing Journal (SCJ)
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- Graphs Theory, Wiener Index

The Wiener Index, or the Wiener Number, also known as the "sum of distances" of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied... more

We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the Wiener maximum quadratic assignment problem, is NP-hard in the ordinary sense and solvable in pseudo-polynomial time.

Results gathered from a monitoring programme on the Mondego Estuary (Western Coast of Portugal) were compliant with findings drawn from other studies, which pointed out that unstable environments, namely estuarine systems, constitute a great challenge for the use of environmental tools such as ecological indices. The Margalef Index, the Shannon-Wiener Index and AMBI were proposed to evaluate the ecological status of benthic communities in the scope of the European Water Framework Directive (WFD) in Portugal and other European member states. In this system these indices were not equally effective in tracking changes in benthic communities that expressed obvious responses to anthropogenic disturbances (eutrophic situations and severe physical disturbance) and to subsequent impacts' cessation. Natural variability played an important role on the indices' response, with estuarine gradient and habitat heterogeneity affecting the ranges of values obtained, and with extreme climate events slowing down the ongoing recovery process. Nonetheless, both natural and anthropogenic variability during the study period could be satisfactorily detected if we accounted for the information provided by all three indices. Based on the whole range of variation observed (a) as a response to different kinds of impacts, and (b) along recovery gradients, as well as accounting for the natural driving forces acting upon estuarine benthic invertebrate communities, we propose a set of reference values for these three indices. This proposal aims at contributing to the implementation of classification tools within the scope of the European WFD.

General formulas for calculating the Wiener index (W) 2 and the hyper-Wiener index (R)3 in spiro-graphs containing three- to six-membered rings are proposed. They are derived on the basis of Hosoya's formula4 and the Klein-Lukovitz-Gutman5 formula for evaluatingW andR, respectively, in cycle-containing graphs, by using the layer matrix of cardinality (LC). 6 An extension of the Wiener number, theW * number of Gutman7 is also evaluated for these spiro-graphs.

- by Bazil Parv
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- CHEMICAL SCIENCES, Wiener Index

The hyper-Wiener index was recently introduced by RandiC. The original definition given by RandiC can be used for acyclic structures only. In this paper the definition of RandiC was extended in two different fashions so as to be applicable for any connected structure. The formula provides an easy method to calculate the hyper-Wiener index for any graph.

In forests where large, stand-replacing disturbances are infrequent, small-scale disturbances associated with the mortality and replacement of individual trees are a primary source of heterogeneity in forest composition and structure. The disturbances considered in this study were canopy gaps created by a partial harvest in the winter of 1987±1988 in an oak±pine (Quercus± Pinus) forest that is part of a long-term ecosystem study at the Holt Research Forest in coastal Maine. This study examined the gap phase of the forest turnover cycle: the brief episodes of rapid change when processes determining the structure and composition of a forest community occur. The objective was to evaluate the effects of harvest-created gaps and soil moisture (as re¯ected by soil drainage classes) on woody and herbaceous species diversity, composition, and abundance relative to unharvested control areas. Because the vegetation was sampled in both 1993 and 1998, detection of short-term changes was possible.

- by Jack Witham
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- Regeneration, Forest Ecology And Management, Ecology, Biodiversity

Poplar plantations host a number of organisms which can live and reproduce in this habitat. Among these, ground beetles (Coleoptera, Carabidae) show strict relations with the environmental conditions and are therefore potential bioindicators of the ecosystem stability or stress. For this reason ground beetle assemblages have been studied for about 10 years (1989±1999) in poplar stands of different ages in the Po Valley (Italy) as well as in reference habitats, i.e. natural woods and agricultural crops, in order to assess their potential as indicators of anthropogenic impact. Sampling was carried out by homogeneous pitfall trapping. The number of species in each assemblage varied between 10 and 46, without any recognisable correlation with factors such as habitat type or age of thepoplar stand; even theShannon±Wienerindex was extremelyvariableandin nowaycorrelatedwith the factorsabove. Evenness values were generally quite low in all poplar plantations, due to the simpli®ed dominance structures of these carabid assemblages, which are characterised by only a few dominant and sub-dominant species; on the contrary, in natural woods the quantitative distribution of species within the community was fairly well balanced. The forest af®nity index (FAI) is a newly proposed ecological index which expresses an evaluation of the relative quality of a habitat compared to another reference habitat; in the case of poplar plantations, which are basically a woody agricultural crop, the FAI index is devised to measure their similarity with (or distance from) natural woodlands. This index displayed a high variability; nevertheless in a linear regression model it appeared to be signi®cantly dependent on the age of the poplar stands. FAI values ranged between À0.35 and À0.45 in agricultural crops and in young poplar stands, and was positive only in a few 7-year-old (and older) poplar plantations (top value 0:25); on the contrary the FAI index was highly positive in natural woods (top value 0:92 in a beech wood). Increasing FAI values in poplar stands throughout the cultural cycle are due totheimmigration of morespecialised forest carabid species,even ifthey neverreachthevaluestypical offoresthabitats. In conclusion, the FAI index proved to be the only parameter potentially useful to assess the ecological complexity of poplar stands. #

- by Riccardo Sciaky
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- Forest Ecology And Management, Ecology, Biodiversity, Stability

Organic farming is considered an important way to preserve biodiversity in agricultural landscapes. However, more work is still necessary to enable a full appraisal of the potential benefits of this way of farming, since studies differ in the evaluation of its effectiveness. Studies are particularly scarce in the Mediterranean region, where different climatic and ecological conditions prevent simple extrapolations from work carried out at northern latitudes. In the present study, an analysis of weed and arthropod communities was conducted in 28 pairs of organic and conventional fields in a dry cereal farmland in central Spain. Plants were identified to the species level, and arthropods to the family level. Pitfalls and sweep nets were used to sample respectively, ground-dwelling and plant-visiting arthropods. Abundance (total numbers of individuals), richness (total numbers of plant species or arthropod families), diversity (Shannon-Wiener index) and biomass (milligrams per pitfall/sweep-net) were calculated for each field and compared between organic and conventional fields using Generalized Linear Mixed Models (GLMMs). To explore the effect of predictor variables on weed richness and arthropod biomass, GLMMs were used. Organic fields showed higher abundance of weeds and arthropods (3.01 and 1.43 times, respectively), higher weed richness and diversity (2.76 and 2.33 times, respectively), and a 24% reduction in cereal plants. Arthropod diversity was lower in organic fields due to the presence of three dominant groups: Collembola, Chloropidae (Diptera), and Aphididae (Hemiptera). Weed richness increased as cereal cover decreased in organic fields. Total arthropod biomass was slightly higher in organic fields, and was affected by weed abundance and diversity. The differences between organic and conventional fields found in this study were higher than those reported for northern latitudes. This could be explained by the richer weed flora in the Mediterranean region, and a higher weed seed availability favored by the two-year rotation system typical of Iberian dry cereal farmland. We conclude that organic farming may contribute to preserve biodiversity in dryland cereal agroecosystems in the Mediterranean region.

- by carolina Bravo
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- Organic agriculture, Ecology, Organic Farming, Environmental Sciences

The hyper Wiener index of the connected graph G is

- by Ali Iranmanesh
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- Applied Mathematics, Combinatorics, Optimization, Distance

a b s t r a c t Eliasi and Taeri [Extension of the Wiener index and Wiener polynomial, Appl. Math. Lett. 21 (2008) 916-921] introduced the notion of y-Wiener index of graphs as a generalization of the classical Wiener index and hyper Wiener index of graphs. They obtained some mathematical properties of this new defined topological index. In this paper, the join, Cartesian product, composition, disjunction and symmetric difference of graphs under y-Wiener index are computed. By these results most parts of a paper by Sagan et al. [The Wiener polynomial of a graph, Int. J. Quant. Chem. 60 (1996) 959-969] and another paper by Khalifeh et al. [The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008) 1402-1407] are generalized.

- by Samaneh Hossein-zadeh
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- Applied Mathematics, Topological Index, Wiener Index

Grasslands are usually the most suitable environment for butterflies, but have been also traditionally used for productive activities. This paper compares the impact of mowing and grazing on butterfly biodiversity in two S Italian (Campania) grasslands, at Campo Somma (CS) and Pianoro di Prada (PP) located at an identical altitude of 850 m. These grasslands have an area of approximately 6 ha each and are at a 3 km distance from each other. They share similar climate and are both surrounded by woods, mainly of sweet chestnut. CS is managed for haying and is mown once a year, in June. PP is used for sheep and cattle grazing. Weekly transects were made from

- by Irene Stanislao and +2
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- Ecology, Biodiversity, Biodiversity Conservation, Cattle Grazing

- by Alireza Ashrafi
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- Applied Mathematics, Topological Index, Wiener Index

The advance of agricultural frontier may cause the Cerrado (Brazilian savanna) to disappear before 2030. This work focuses on measuring the impact of pasture implantation on a cerrado's termite fauna. Termites were sampled in a cerrado sensu stricto and a pasture, originally cerrado. All species were classified as their feeder group, accumulation curves were made and Shannon-Wiener indexes and b diversity were calculated for both areas. Cerrado was richer than pasture and species composition differed considerably, leading b diversity to a high value. The humivorous was the most representative species, followed by grass/litter feeders, xylophagous and, less representative, the intermediates. There were more xylophagous and intermediates species on cerrado than in pasture; the grass/litter feeders were more abundant in pasture, but didn't differed in number or species; and humivorous didn't differed neither in richness nor in abundance. This work shows that the simplification of the habitat is indeed causing the extinction of populations that depend on some specifics resource.

- by Tiago Carrijo
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- Biological Sciences, Environmental Sciences, Insect Conservation, Abundance

The distance d (u,v) between two vertices u and v of a connected graph G is equal to the length of a shortest path that connects u and v. The Hosoya polynomial was introduced by H. Hosoya in 1988 and defined as , . In this paper, we compute the Hosoya polynomial of Harary graph. Also we compute the Wiener index and hyper Wiener index of this family of Regular graphs.

- by Mohammad Reza Farahani
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- Wiener Index

Etant donné leur texture sableuse, les sols de la zone côtière de la province de Thua Thien Hue au Centre Vietnam présentent un milieu particulier pour le développement des organismes du sol, dont les vers de terre représentent 70% de la biomasse. Cette étude met en relation les caractéristiques du sol et les communautés de vers de terre, après identification de ceux-ci. Sept espèces appartenant aux familles des Glossoscolecidae, des Megascolecidae et des Microchaetidae ont été relevées : Pontoscolex corethrurus, Glyphidrilus papillatus, Pheretima rodericensis, Pheretima danangana, Pheretima sp., Perionyx excavatus, et Lampito mauritii. Les Microchaetidae sont présents quelque soit la richesse du sol et constituent la famille dominante dans les sols acides à forte teneur en limon et argile. Les deux autres familles sont associées à des sols pauvres mais moins acides, riches en sable. Il ressort également de cette étude que le nombre de P. corethrurus est significativement plus important dans les vergers (AF) alors que L. mauritii est significativement plus présent dans les sols avec des autres cultures que le riz (AC). G. papillatus, significativement plus abondant dans les friches, est la seule espèce retrouvée dans ce milieu. L'étude de la diversité (Indice de Shannon-Wiener) montre que les cultures autres que le riz (AC) présentent la plus grande diversité de vers de terre (H' = 0,97) alors que les friches ne présentent aucune diversité.

- by pham tu
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- Biology, Vietnam, Potato, Sol

During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener index and Wiener polynomial for threshold graphs.

- by Elena Nechita
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- Wiener Index, Threshold graph, Wiener polynomial

Inverse gas chromatography is currently used for the determination of the surface properties of divided solids by probing the surface with alkanes or polar molecules of known properties. This paper suggests the use of a new topological... more

- by Eric BRENDLE
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- Engineering, Topological Index, Gibbs Free Energy, Physical sciences

is a tropical country that has adopted biological monitoring using macroinvertebrates and has adapted the BMWP score for its water bodies, where the new score is named BMWP-CR. In an experimental survey to assess the application of the BMWP-CR score, we considered seven study sites with a gradient of anthropogenic activities along the Dos Novillos river. The Shannon-Wiener Diversity and Pielou Evenness indexes were computed. The first study site was considered as the reference site. Four taxonomic groups were detected: Annelida, Platyhelminthes, Mollusca and Arthropoda. The last group was the most abundant and diverse. The Shannon-Wiener index ranged between 1.14 in a study site close to a banana processing facility, to 3.49 in a study site near to the confluence of the Dos Novillos River with the Parismina river. In such study sites, the Pielou Evenness index values varied from 0.57 to 0.83, respectively. The BMWP-CR scores ranged from 24 in the study site near the banana processing facility, to 116, in a downstream study site, reaching values higher than the reference site selected upstream in the Dos Novillos river far away from anthropogenic influence. Insects were the most diverse and abundant group. The correlation between the Shannon-Wiener Diversity index and the BMWP-CR scores presented a high significance value (R 2 = 0.927). Therefore, we suggest that the Shannon-Wiener index can be used alongside the BMWP-CR scores. The BMWP-CR method is sensitive enough for detecting changes in water quality reflecting differences in land uses along the studied river. RESUMEN: Macoinvertebrados bénticos como indicadores de la calidad del agua en corrientes de Costa Rica: Usando una adaptación del puntaje BMWP. Costa Rica es uno de los países de latitudes tropicales que ha adoptado el monitoreo biológico y adaptado el BMWP para sus cuerpos de agua, denominándolo BMWP-CR. En un estudio experimental para evaluar la aplicación del BMWP-CR, consideramos siete sitios de estudio dentro de un gradiente de actividades antropogénicas en el río Dos Novillos. Los índices de diversidad de Shannon-Wiener y de equidad de Pielou fueron también calculados. El primer sitio de estudio fue considerado como sitio de referencia. Se detectó la presencia de cuatro grandes grupos taxonómicos: Anélidos, Platelmintos, Moluscos y Artrópodos. Este último fue el más abundante y diverso. El índice de Shannon-Wiener varió de 1.14 en un sitio cercano a una planta procesadora de bananos, hasta 3.49 en un sitio de estudio cercano a la REZUMAT: Macronevertebratele bentonice ca indicatori ai calităţii apei în râuri din Costa Rica: utilizând o adaptare a indexului BMWP. Costa Rica este o ţară tropicală care a adoptat monitoringul biologic, utilizând macronevertebratele şi a adaptat BMWP pentru râuri; noul indice adaptat poartă denumirea BMWP-CR. Într-un studiu experimental, pentru a evalua aplicarea indicelui BMWP-CR, s-au luat în considerare şapte situri cu un gradient al activităţilor antropice de-a lungul râului Dos Novillos. Au fost calculaţi indicele Shannon-Wiener şi indicele de uniformitate Pielou. Primul sit a fost considerat ca sit de referinţă. Au fost identificate patru grupe taxonomice: anelide, platelminţi, moluşte şi artropode. Artropodele au fost cele mai abundente şi diverse ca specii. Indicele Shannon-Wiener are valori de la 1,14 (într-un studiu de caz, aflat în apropierea unor facilităţi de procesare a bananelor) la 3,49 într-un sit din apropierea confluenţei râului Dos Novillos cu râul Parismina. În aceleaşi situri, valoare indicelui Pielou este de 0,57, respectiv 0,83. Indicele BMWP-CR, în aceleaşi situri are valorile 24 în apropierea locului de procesare a bananelor, respectiv 116 în aval, astfel ajungând la valori mai mari decât în situl de referinţă (localizat în amontele râului Dos Novillos, departe de activităţi antropice). Insectele au fost cel mai divers şi abundent grup. Corelaţia valorilor indicelui Shannon-Wiener cu indicele BMWP-CR au prezentat o valoare cu o semnificaţie ridicată (R2= 0.927). De aceea, propunem ca indicele Shannon-Wiener să se utilizeze alături de indicele BMWP-CR. Indicele BMWP-CR este suficient de "sensibil" ca să poată fi utilizat pentru a identifica modificarea calităţii apei, reflectând diferenţele în utilizarea terenurilor de-a lungul râului studiat.

- by Bert Kohlmann
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- Water quality, Ecology, Transylvanian Romanians, River Basin

Narezushi, a derivation of sushi, is a traditional Japanese food made by fermenting salted fish meat and cooked rice together. In this study, the microbial diversity of saba-narezushi (narezushi of mackerel, Scomber japonicus) was analyzed by the 16S ribosomal RNA gene clone library method. Chemical composition was also analyzed to compare with different kinds of narezushi. The chemical composition of the narezushi was similar to those obtained from samma-narezushi. Ninety-four clones were randomly selected and DNA sequences of cloned fragments (approx. 890 bp) were analyzed. The DNA sequences obtained were phylogenetically analyzed. The expected operational taxonomy units (OTUs) by Chao1 estimates and Shannon-Wiener index (H′) at 97% identity threshold were 48 and 1.822, respectively. The sequence similarity of the cloned fragment was equal to or higher than 98% of the sequence of cultivated bacterial species in the public database. Most of the clones (85%) belonged to lactic acid bacteria (LAB). Lactobacillus curvatus was the most abundant species followed by Lactococcus piscium and Leuconostoc gasicomitatum, suggesting that these bacteria play important roles in the fermentation of saba-narezushi.

- by Ayu Chan
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- Microbial diversity, Food Science and Technology, Gene Cloning, Lactic Acid Bacteria

In this work, we have made an attempt to derive a novel information theoretic topological index, net-sign identity information index, I e from the molecular electronic structure, proposed by Lee et al. Chem. Phys. Lett., 137 (1987) 279] in chemical graph theory. The performance of the net-sign identity information index along with the square root of the bonding information index, p I b and the square root of net-sign identity information index, p I e have been compared with the most widely used molecular descriptors: Wiener index (W), Randic's connectivity index (v) and Balaban's distance sum connectivity index (J) in QSPR modeling.

- by Prabhat Kumar Sahu
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- Technology, Graph Theory, Molecular Electronics, Topological Index