Cactus graphs with minimum edge revised Szeged index

The edge revised Szeged index Sz(e)*(G) is defined as Sz(e)*(G) = Sigma(e=uv is an element of E)(M-u(e) + m(0)(e)/2) (m(v) (e)+ m(0)(e)/2), where m(u)(e) and m(v)(e) are, respectively, the number of edges of G lying closer to vertex u than to vertex v and the number of edges of G lying closer to vertex v than to vertex u, and Inge) is the number of edges equidistant to u and v. A cactus graph is a connected graph in which every block is an edge or a cycle. In this paper, we give a lower bound of the edge revised Szeged index among all m-edges cactus graphs with k cycles, and also characterize those graphs that achieve the lower bound. We also obtain the second minimum edge revised Szeged index for connected cactus graphs of size m with k cycles. (C) 2018 Elsevier B.V. All rights reserved.