Neighborhood Versions of Geometric–Arithmetic and Atom Bond Connectivity Indices of Some Popular Graphs and Their Properties

Abstract

In this article, we introduce the neighborhood versions of two classical topological indices, namely neighborhood geometric–arithmetic and neighborhood atom bond connectivity indices. We study the graph-theoretic properties of these new topological indices for some known graphs, e.g., complete graph Kn, regular graph Rn, cycle graph Cn, star graph Sn, pendant graph, and irregular graph and further establish their respective bounds. We note that the neighbourhood geometric–arithmetic index of Kn, Rn, Cn, and Sn is equal to the number of edges. The neighborhood atom bond connectivity index of an arbitrary simple graph G is strictly less than the number of edges. Our results contribute to the literature in this direction.