More on inverse degree and topological indices of graphs

Abstract

The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of vertex degrees of the graph G. In this paper, we obtain several lower and upper bounds on inverse degree ID(G). Moreover, using computational results, we prove our upper bound is strong and has the smallest deviation from the inverse degree ID(G). Next, we compare inverse degree ID(G) with topological indices (Randić index R(G), geometric-arithmetic index GA(G)) for chemical trees and also we determine the n−vertex chemical trees with the minimum, the second and the third minimum, as well as the second and the third maximum of ID − R. In addition, we correct the second and third minimum Randić index chemical trees in [16].