Real-Number Vertex Invariants and Schultz-Type Indices Based on Eigenvectors of Adjacency and Distance Matrices (original) (raw)

Topological indices and real number vertex invariants based on graph eigenvalues or eigenvectors

Journal of Chemical Information and Modeling, 1991

Eigenvectors obtained from the adjacency or distance matrix of graphs, corresponding to the largest negative eigenvalue, are useful real number vertex invariants for intramolecular ordering of vertices. From them or from eigenvalues, several new topological indices have been tested on the basis of intermolecular ordering of isomeric alkanes and of correlating ability with properties such as the boiling temperature.

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].

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

Computation of Vertex Degree-Based Molecular Descriptors of Hydrocarbon Structure

Journal of Chemistry, 2022

Topological indices are such numbers or set of numbers that describe topology of structures. Nearly 400 topological indices are calculated so far. The prognostication of physical, chemical, and biological attributes of organic compounds is an important and still unsolved problem of computational chemistry. Topological index is the tool to predict the physicochemical properties such as boiling point, melting point, density, viscosity, and polarity of organic compounds. In this study, some degree-based molecular descriptors of hydrocarbon structure are calculated.

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)

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.

New local vertex invariants and molecular descriptors based on functions of the vertex degrees

2010

Abstract Different kinds of Local Vertex Invariants (LOVIs) derived from vertex degrees were reviewed and investigated by comparison. Novel LOVIs, based on a multiplicative form of some vertex degrees defined in literature were also proposed. A data set comprised of 730 diverse molecules with 383 different atom types was used to study similarity/diversity of 17 different LOVIs by Principal Component Analysis.

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.

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.