Topological indices and real number vertex invariants based on graph eigenvalues or eigenvectors (original) (raw)
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Journal of Chemical Information and Modeling, 1998
Eigenvectors corresponding to the lowest eigenvalue of adjacency and distance matrices are used to generate new real-number local vertex invariants (LOVIs), by applying a Schultz-type algorithm. The intramolecular ordering of vertices was tested. From these LOVIs, several new topological indices have been defined and tested on the basis of intermolecular ordering of isomeric alkanes. Correlation with properties such as the normal boiling temperature and octane numbers have also been studied.
Three New/Old Vertex–Degree–Based Topological Indices
Three vertex-degree-based graph invariants are presented, that earlier have been considered in the chemical and/or mathematical literature, but that evaded the attention of most mathematical chemists. These are the reciprocal Randić index (RR), the reduced second Zagreb index RM 2 , and the reduced reciprocal Randić index (RRR). If d 1 , d 2 , . . . , d n are the degrees of the vertices of the graph G = (V, E), then
Degree Based Topological Indices of Isomers of Organic Compounds
Let G(V,E) be a connected graph. The sets of vertices and edges of G are denoted by V=V (G) and E=E (G) respectively. In such a molecular graph, vertices represent atoms and edges represent bonds. The number of edges incident on a vi is called the degree d(vi) of vertex vi . The sum of degrees of all vertices in G is twice the number of edges in G [1]. In molecular graph we have many topological indices. In this research, we computing Randic index, Molecular topological index ,Augmented Zagreb index ,Geometric-Arithmetic index ,Atom– bond connectivity index, Harmonic index ,Sum-connectivity index of n-decane ,3,4,4-Trimethyl heptane and 2,4-dimethyl-4- ethyl hexane.
A Graph Theoretical Method for Partial Ordering of Alkanes
Croatica Chemica Acta, 2007
The topological Zagreb index M 1 introduces an ordering on the set of alkanes. Recently, modified Zagreb indices l M 1 have been proposed, and it is noted that they differently order alkanes. In this paper, the level of consistency between these orders is analyzed. A new partial order f as the intersection of all partial orders l M 1 (where m is at least 2) is introduced and its properties are analyzed. Keywords Zagreb index M 1 modified Zagreb index l M 1 partial order CROATICA CHEMICA ACTA CCACAA 80 (2) 169¿179 (2007)
Role of Multiplicative Degree Based Topological Invariants in Chemical Graphs
A chemical graph is a mathematical representation of a chemical compound in which atoms and bonds are represented by nodes and lines respectively. Chemists have developed a number of useful tools from graph theory, such as topological index (TI) is structural descriptor or connectivity index used to express molecular size, branching, heat of formation, boiling points, strain energy, toughness and acyclicity. The Topological index is beneficial to establish an association between arrangement and chemical properties of chemical compounds without performing any testing. It is characterized into various categories like degree, distance, spectrum and eccentricity based. This paper consists of computation of multiplicative degree based topological indices namely multiplicative Zagreb indices, multiplicative atom bond connectivity index and generalized multiplicative geometric arithmetic index for SiC_3-I[j, k] and SiC_3-II[j, k].
On Degree-Based Topological Indices of Symmetric Chemical Structures
Symmetry
A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randi c ´ , atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randi c ´ index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.
Eccentricity-Based Topological Invariants of Some Chemical Graphs
Atoms, 2019
Topological index is an invariant of molecular graphs which correlates the structure with different physical and chemical invariants of the compound like boiling point, chemical reactivity, stability, Kovat’s constant etc. Eccentricity-based topological indices, like eccentric connectivity index, connective eccentric index, first Zagreb eccentricity index, and second Zagreb eccentricity index were analyzed and computed for families of Dutch windmill graphs and circulant graphs.
On Highly Discriminating Molecular Topological Index
Journal of Chemical Information and Modeling, 1996
A highly discriminating molecular topological index, EAID, is proposed based on the extended adjacency matrix. A systematic search for degeneracy was performed for 3 807 434 alkane trees, 202 558 complex cyclic or polycyclic graphs, and 430 472 structures containing heteroatoms. No counterexamples (two or more nonisomorphic structures with the same EAID number) were found. This is a hitherto unheard of power of discrimination. Thus EAID might be possibly used as supplementary reference for CAS Registry Numbers for structure documentation.
SOME TOPOLOGICAL INDICES DERIVED FROM THE v mdn MATRIX. PART 9. THE Mj(m,n) AND Mij(m,n) INDICES
The Mj(m,n) and Mij(m,n) indices considered here are derived from the v m d n matrix by multiplication of its non-diagonal elements. A general characteristic of the Mj(m,n) and Mij(m,n) indices is the transition domain in the plane of exponents m and n, which is placed along the diagonal characterized by m = -n. Above this diagonal transition domain the values of the Mj(m,n) and Mij(m,n) indices of alkanes increase with the size of the molecule and decrease with branching, whereas the revers e is true below the diagonal. Correlation of tested Mj(m,n) and Mij(m,n) indices with the physicochemical properties of alkanes is better than r = 0.9 in 15 resp. 13 of 23 cases when alkanes from propane to octanes inclusive are considered, as well as in 12 resp. 8 of 24 cases when only octanes are taken into account. There is a number of Mj(m,n) and Mij(m,n) indices that have a regular sequence of isomers due to increasing branching. In the plane of exponents m and n they are positioned in th...
On Valency-Based Molecular Topological Descriptors of Subdivision Vertex-Edge Join of Three Graphs
Symmetry
In the studies of quantitative structure–activity relationships (QSARs) and quantitative structure–property relationships (QSPRs), graph invariants are used to estimate the biological activities and properties of chemical compounds. In these studies, degree-based topological indices have a significant place among the other descriptors because of the ease of generation and the speed with which these computations can be accomplished. In this paper, we give the results related to the first, second, and third Zagreb indices, forgotten index, hyper Zagreb index, reduced first and second Zagreb indices, multiplicative Zagreb indices, redefined version of Zagreb indices, first reformulated Zagreb index, harmonic index, atom-bond connectivity index, geometric-arithmetic index, and reduced reciprocal Randić index of a new graph operation named as “subdivision vertex-edge join” of three graphs.