On the Wiener index of unicyclic graphs with given girth.

The Wiener index of a graph G is defined as W(G) = Sigma(u,v epsilon V(G)) d(G)(u,v), where d(G)(u, v) is the distance between u and v in and the sum goes over all the pairs of vertices. In this paper, we investigate the Wiener index of unicyclic graphs with given girth and characterize the extremal graphs with the minimal and maximal Wiener index.