On the Szeged index of unicyclic graphs with given diameter

The Szeged index of a connected graph G is defined as S-z(G) = Sigma(e=uv is an element of E(G)) n(u)(e|G)n(v)(e|G), where E(G) is the edge set of G, and for any e = uv is an element of E(G), n(u)(e|G) is the number of vertices of G lying closer to vertex u than to v, and n(v)(e|G) is the number of vertices of G lying closer to vertex v than to u. In this paper, we characterize the graph with minimum Szeged index among all the unicyclic graphs with given order and diameter. (C) 2017 Elsevier B.V. All rights reserved.