On the difference between the (revised) Szeged index and the Wiener index of cacti

A connected graph is said to be a cactus if each of its blocks is either a cycle or an edge. Let cen be the set of all n-vertex cacti with circumference at least 4, and let l(n,k) be the set of all n -vertex cacti containing exactly k >= 1 cycles where n >= 3k + 1. In this paper, lower bounds on the difference between the (revised) Szeged index and Wiener index of graphs l(n) (resp.l(n,k)) are proved. The minimum and the second minimum values on the difference between the Szeged index and Wiener index of graphs among,e are determined. The bound on the minimum value is strengthened in the bipartite case. A lower bound on the difference between the revised Szeged index and Wiener index of graphs among l(n,k) is also established. Along the way the corresponding extremal graphs are identified. (C) 2018 Elsevier B.V. All rights reserved.