On inverse degree and topological indices of graphs

Abstract

Let G = (V; E) be a simple graph of order n and size m with maximum degree Δ and minimum degree δ. The inverse degree of a graph G with no isolated vertices is defined as (Formula presented)where di is the degree of the vertex vi ∈ V(G). In this paper, we obtain several lower and upper bounds on ID(G) of graph G and characterize graphs for which these bounds are best possible. Moreover, we compare inverse degree ID(G) with topological indices (GA1-index, ABC-index, Kf -index) of graphs.