On the Szeged index of unicyclic graphs with given diameter

The Szeged index of a connected graph G is defined as Sz(G)=∑e=uv∈E(G)nu(e|G)nv(e|G),where E(G) is the edge set of G, and for any e=uv∈E(G), nu(e|G) is the number of vertices of G lying closer to vertex u than to v, and nv(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.