COMPUTING DEGREE BASED TOPOLOGICAL INDICES OF SIERPINʹSKI GRAPHS1 (original) (raw)

Degree Based Topological Indices of a General Random Chain

arXiv (Cornell University), 2022

Let G = (V (G), E(G)) a graph, many important topological indices can be defined as T I(G) = vu∈E(G) h(d v , d u). In this paper, we look at one type of general random chains and an alternative approach to study these kinds of topological indices is proposed. In which their explicit analytical expressions of the expected values and variances are obtained. Moreover, the asymptotic normality of topological indices of a random chain is established through the Martingale Central Limit Theorem.

On the general zeroth-order Randić index of bargraphs

2019

In graph theory, an invariant of a graph is a numerical quantity that depends only on its abstract structure, not on graph representations such as particular labeling or drawing of the graph. A topological index is an invariant of a molecular graph associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Nowadays, there exists a legion of topological indices with some applications in chemistry, especially in QSAR (quantitative structure-activity relationship) and QSPR (quantitative structure-property relationship) studies [18]. Since topological indices have gained considerable popularity recently, many new topological indices have been proposed and studied in the mathematical chemistry literature. In 1975, Randić introduced the connectivity index [17], which is one of the the most studied and applied topological indices in QSPR and QSAR researches, defined by

On Generalized Topological Indices for Some Special Graphs

Journal of Mathematics

Topological indices are numeric values associated with a graph and characterize its structure. There are various topological indices in graph theory such as degree-based, distance-based, and counting-related topological indices. Among these indices, degree-based indices are very interesting and studied well in literature. In this work, we studied the generalized form of harmonic, geometric-arithmetic, Kulli–Basava indices, and generalized power-sum-connectivity index for special graph that are bridge graph over path, bridge graph over cycle, bridge graph over complete graph, wheel graph, gear graph, helm graph, and square lattice graph. We found exact values for the stated indices and for the stated special graphs. We also investigated the generalized form of the indices for various properties of alkane isomers, from which we obtained interesting results which are closed to that of experimental obtained results.

On Sum Degree-Based Topological Indices of Some Connected Graphs

Mathematical Problems in Engineering

In mathematical chemistry, molecular structure of any chemical substance can be expressed by a numeric number or polynomial or sequence of number which represents the whole graph is called topological index. An important branch of graph theory is the chemical graph theory. As a consequence of their worldwide uses, chemical networks have inspired researchers since their development. Determination of the expressions for topological indices of different derived graphs of graphs is a new and interesting problem in graph theory. In this article, some graphs which are derived from honeycomb structure are studied and obtained their exact results for sum degree-based indices. Additionally, a comparison is shown graphically among all the indices.

On some bounds of the topological indices of generalized Sierpiński and extended Sierpiński graphs

Journal of Inequalities and Applications

Sierpiński graphs are extensively studied graphs of fractal nature with applications in topology, mathematics of Tower of Hanoi and computer science. The generalized Sierpiński graphs are defined by replication of exactly the same graph, yielding self-similar graph. Certain graph invariants referred to as topological indices are used to determine a large number of properties like physico-chemical properties, thermodynamic properties, chemical activity and biological activity of chemical graphs. In QSAR/QSPR study, these graph invariants play a vital role. In this article, we study the topological indices of generalized Sierpiński and extended Sierpiński graphs with an arbitrary base graph. We obtain bounds for the atom-bond connectivity index, harmonic index, Zagreb indices and sum-connectivity index for the generalized Sierpiński graphs and extended Sierpiński graphs.

On a variation of Randic index

Australasian Journal of Combinatorics

Randic index, R, also known as the connectivity or branching index, is an important topological index in chemistry. In order to attack some conjectures concerning Randic index, Dvorak et al. introduced a modification of this index, denoted by R'. In this paper we present some of the basic properties of R'. We determine graphs with minimal and maximal values of R', as well as graphs with minimal and maximal values of R' among the trees and unicyclic graphs. We also show that if G is a triangle-free graph on n vertices with minimum degree d, then R'(G) >=d. Moreover, equality holds only for the complete bipartite graph.

Bounds for the Topological Indices of ℘ graph

2021

Topological indices are mathematical measure which correlates to the chemical structures of any simple finite graph. These are used for Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR). In this paper, we define operator graph namely, ℘ graph and structured properties. Also, establish the lower and upper bounds for few topological indices namely, Inverse sum indeg index, Geometric-Arithmetic index, Atom-bond connectivity index, first zagreb index and first reformulated Zagreb index of ℘-graph.

The Degree-Based Topological Indices for Two Special Families of Graphs of Diameter Three

Advances in Mathematical Physics, 2021

In this research article, we determine some vertex degree-based topological indices or descriptors of two families of graphs, i.e., G = C 4 ðK n Þ and G = C 4 ðK n Þ + v 1 v 3 , where C 4 ðK n Þ is a graph obtained by identifying one of the vertices of K n with one vertex of C 4. Similarly, a graph formed by joining one of the vertices of K n with one vertex of C 4 + v 1 v 3 is known as the C 4 ðK n Þ + v 1 v 3 graph.

Some theorems about the Randic connectivity index

We derive some basic facts about the Randić connectivity index. Many corollaries for chemical graphs are then discussed -in particular, we give exact formulae for benzenoids, coronoids, and diamondoids which depend only on the frequency of certain edge types. Many of these results about benzenoids are rediscoveries -but we generalize them to larger families of graphs and shorten and simplify the arguments.