Abstract
Sierpinski graphs are a widely observed family of fractal-type graphs relevant to topology, Hanoi Tower mathematics, computer engineering, and around. Chemical implementations of graph theory establish significant properties, such as chemical activity, physicochemical properties, thermodynamic properties, and pharmacological activities of a molecular graph. Specific graph descriptors alluded to as topological indices are helpful to predict these properties. These graph descriptors have played a key role in quantitative structure-property/structure-activity relationships (QSPR/QSAR) research. The objective of this article is to compute Randic index ( R − 1 / 2 ), Zagreb index M 1 , sum-connectivity index SCI , geometric-arithmetic index GA , and atom-bond connectivity ABC index based on ev-degree and ve-degree for the Sierpinski networks S n , m .
Highlights
Graph theory is concerned with network of points connected by lines. e beginning of graph theory deals with recreational math problems, but it has grown into significant research area
Scientists are very attentive to know about the topology of chemical networks through some mathematical parameters gained from the network graphs of chemical molecules
A large scale of topological indices has been examined in biochemistry through QSPR/QSAR analysis to analyze chemical networks topology related to pharmacy, medical engineering, and experimental science, which are important fields of Chemical graph theory (CGT) [1]
Summary
Graph theory is concerned with network of points connected by lines. e beginning of graph theory deals with recreational math problems, but it has grown into significant research area. Topological indices are numerical numbers associated with the networks that can be helpful to predict some of its Mathematical Problems in Engineering properties. First degree-based topological index was proposed by Randic [5] in 1975 and named as “branching index.” It was later called as Randic connectivity indexR(− 1)/2(H). We denote the ev-degree of an edge u1v1 e1 ∈ E(H) by Λev(e1) and is defined as the cardinality of the set N[u1] ∪ N[v1]. The ve-degree type first Zagreb beta (Mβ1ve) index, geometric-arithmetic (GAve) index, atom-bond connectivity (ABCve) index, second Zagreb (Mv2e) index, sumconnectivity (χve) index, Randic (Rve) index, and harmonic (Hve) index for each edge u1v1 ∈ E(H) are defined as. E objective of this paper is to calculate exact values of topological indices for Sierpinski network S(n, m) based on ve- and ev-degree A lot of research is going on these topological indices. e results related to these topological indices can be found in [21,22,23,24,25]. e objective of this paper is to calculate exact values of topological indices for Sierpinski network S(n, m) based on ve- and ev-degree
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