Some bounds on balaban index of a graph

Abstract

The Balaban index of a graph G is defined as m/(μ+1) σ_e+uv[d(u)d(v)]^-0.5, where m is the number of edges of G, μ is the cyclomatic number of G and for every vertex x of G, d(x) is the summation of distances between x and all vertices of G. Zhou and Trinajstic obtained some tight upper and lower bounds for the Balaban index [see Croat. Chem. Acta 81 (2008) 319-323.] In this paper, we continue this work and apply Aczel and Ozeki inequalities to find some new upper and lower bounds for this topological index.