Degree based Topological indices of Hanoi Graph

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.

Discrete Mathematics Letters, 2021

The atom-bond connectivity (ABC) index was introduced in the last quarter of the 1990s to improve the prediction power of the Randić index. Later on, in 2008, the factor √ 2 was dropped from the original definition of the ABC index, and some additional chemical applications of this index were reported, which resulted in considerable interest in studying the mathematical properties of the ABC index. There are more than a hundred papers devoted to the mathematical aspects of this graph invariant. The primary purpose of this review is to gather the existing bounds and extremal results concerning the ABC index.

Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015), 2016

The atom bond connectivity (ABC) index is one of the recently most investigated degree-based molecular structure descriptors that have applications in chemistry. For a graph G, the ABC index is defined as , where d u denotes the degree of a vertex u in G. In this paper, we obtain the general formula for ABC index of some special, chemical trees, and bicyclic graphs.

Acta Universitatis Apulensis

The atom-bond connectivity index is a topological index was defined as

arXiv (Cornell University), 2023

The atom-bond-connectivity (ABC) index is one of the wellinvestigated degree-based topological indices. The atom-bond sumconnectivity (ABS) index is a modified version of the ABC index, which was introduced recently. The primary goal of the present paper is to investigate the difference between the aforementioned two indices, namely ABS − ABC. It is shown that the difference ABS − ABC is positive for all graphs of minimum degree at least 2 as well as for all line graphs of those graphs of order at least 5 that are different from the path and cycle graphs. By means of computer search, the difference ABS − ABC is also calculated for all trees of order at most 15.

Journal of Molecular Structure-theochem, 1997

2020

There are plenty of topological indices used in chemistry to study the chemical behavior and physical properties of molecular graphs. In the literature, several results are computed for degree based topological indices like “first Zagreb index, second Zagreb index, modified second Zagreb index, generalized Randić index, inverse Randić index, symmetric sum division index, harmonic index, inverse sum index, augmented Zagreb index”. In this paper, we have investigated the aforesaid degree based topological indices for Hanoi graph and generalized wheel graph with the help of M-polynomial.

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

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].

2012

A topological representation of a molecule can be carried out through molecular graph. The descriptors are numerical values associated with chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. A topological index is the graph invariant number calculated from a graph representing a molecule. The most of the proposed topological indices are related either to a vertex adjacency relationship (atom-atom connectivity) in the graph G or to topological distances in G. In this paper we introduce an edge operation ˆ e on the graphs 1 G and 2 G such that resulting graph 12 ˆ Ge G has an edge introduced between arbitrary vertex of 1