Abstract
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 Randić, 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 Randić 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.
Highlights
A graph is formed by vertices and edges connecting the vertices
ABC4 and GA5 indices find only if we find the edge partition of interconnection networks each edge in the graphs depend on sum of the degrees of end vertices
Hex-Derived Cage networks HDCN1(m, n) and HDCN2(m, n) give closed formulas of that indices, we study the general Randić, first Zagreb, atom-bond connectivity (ABC), GA, ABC4 and GA5 indices of certain graphs in [10]
Summary
A graph is formed by vertices and edges connecting the vertices. A network is a connected simple graph having no multiple edges and loops. A topological index is a numerical value associated with chemical constitution for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Many tools, such as topological indices has provided by graph theory to the chemists. In the QSAR /QSPR study, physico-chemical properties and topological indices such as Wiener index, Szeged index, Randić index, Zagreb indices and ABC index are used to predict bioactivity of the chemical compounds. Topological indices were firstly introduced by Wiener [1], he named the resulting index as path number while he was working on boiling point of Paraffin. Estrada et al in [6] invented a very famous degree-based topological index ABC and defined as s.
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