Some topological indices derived from the vmdn matrix. Part 7, The Vij(m,n) indices (original) (raw)
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Some topological indices derived from the vmdn matrix. Part 8, The Lij(m,n) indices
Acta Chimica Slovenica
The S W A (m,n) indices derived from the v m d n matrix raise expectations that at least two groups of them might be good branching indices of BI A type. The indices of one of these groups indicate that a peripherally substituted alkane is more branched than a centrally substituted one, whereas the indices of the other group indicate the reverse. Some of the S W A (m,n) indices correlate well, having r > 0.99, with physicochemical properties ω and Tc/Pc. Several ones have r > 0.9 with BP/Tc, Tc2/Pc, C, ∆Hf°g, Pc, and ∆Hv.
Acta Chimica Slovenica
The S W A (m,n) indices derived from the v m d n matrix raise expectations that at least two groups of them might be good branching indices of BI A type. The indices of one of these groups indicate that a peripherally substituted alkane is more branched than a centrally substituted one, whereas the indices of the other group indicate the reverse. Some of the S W A (m,n) indices correlate well, having r > 0.99, with physicochemical properties ω and Tc/Pc. Several ones have r > 0.9 with BP/Tc, Tc2/Pc, C, ∆Hf°g, Pc, and ∆Hv.
Acta Chimica Slovenica
The S W A (m,n) indices derived from the v m d n matrix raise expectations that at least two groups of them might be good branching indices of BI A type. The indices of one of these groups indicate that a peripherally substituted alkane is more branched than a centrally substituted one, whereas the indices of the other group indicate the reverse. Some of the S W A (m,n) indices correlate well, having r > 0.99, with physicochemical properties ω and Tc/Pc. Several ones have r > 0.9 with BP/Tc, Tc2/Pc, C, ∆Hf°g, Pc, and ∆Hv.
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...
Topological indices derived from the G(a,b,c) matrix, useful as physicochemical property indices
Acta Chimica Slovenica
From the G(a,b,c) matrix at least 20 groups of topological indices can be derived. Each of these groups contains an infinite number of possible indices. Some of these indices correlate by abs(r) max > 0.99, and a number of them by abs(r) max > 0.9 with particular tested 29 resp. 31 physicochemical properties of alkanes. Therefore, their use in QSPR/QSAR models is recommended. The indices of these groups are not useful to predict the physicochemical properties: dc, Zc, A, Cohesive Energy Density, and Solubility Parameter. the non-diagonal matrix elements; original indices raised to several exponents, e.g.
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.
On Certain Degree Based and Bond-Additive Topological Indices of Dodeca-Benzo-Circumcorenene
Combinatorial Chemistry & High Throughput Screening,, 2023
Background: Chemical graph theory has been used to mathematically model the various physical and biological aspects of chemical substances. A mathematical formulation that may be applied to any graph and can characterise a molecule structure is known as a topological index or molecular descriptor. Method: It is convenient and efficient to analyse the mathematical values and further research on various physical properties of a molecule based on these molecular descriptors. They provide useful alternatives to lengthy, expensive, and labour-intensive laboratory experiments. The topological indices can be used to predict the chemical structures, physicochemical properties, and biological activities using quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs). Result: In this study, the molecular descriptors of the Dodeca-benzo-circumcorenene compounds are derived based on their corresponding molecular structures. Conclusion: The computed indices are then compared graphically to study their relationship with the molecular structure and with each other.
Results on the Estrada Indices of Benzenoid Hydrocarbons
Polycyclic Aromatic Compounds, 2020
The spectral moments of the edge adjacency matrix and adjacency matrix recently have been successfully employed in quantitative structureproperty relationship and quantitative structure-activity relationship studies of alkanes, alkyl halides, benzyl alcohols,cycloalkanes and benzenoid hydrocarbons. Let G be a molecular graph with n vertices, m edges and G(L) be a line graph. Both graphs G and G(L) can be represented by their adjacency matrixes A and E, respectively. The eigenvalues of G and G(L) are denoted by, k 1 Pk 2 P Á Á Á Pk n and c 1 Pc 2 P Á Á Á Pc n , respectively. The Estrada index A and G(L) are defined as EEðGÞ ¼ P n i¼1 e ki and EEðGðLÞÞ ¼ P n i¼1 e c i : In this paper, we examined both Estrada indices with spectral moments of the edge adjacency matrix and adjacency matrix of benzenoid hydrocarbons. These theoretical conclusions provide practical guiding significance for pharmaceutical engineering, complex network and quantify the degree of folding of long organic molecules.
On Adriatic Indices and its Application to Some Properties of Alkanes
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The adriatic indices like max-min and min-max deg indices are defined by V.Damir and G.Marija. In this paper we have given certain generalization for some graphs and presented few bounds for these two indices. Along with that some graph operations has been performed like join and corona product. Lastly some chemical applications of max-min and min-max degree indices for alkanes are explored. MSC: 05C07, 05C12, 05C85.
Topological Indices of Certain Transformed Chemical Structures
Journal of Chemistry, 2020
Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.