On the Wiener index of unicyclic graphs

Abstract

The Wiener index of a graph G is defined as W(G) = $Sigma _{u,v} d_G (u, v),$ where $ d_G (u, v)$ is the distance between u and v in G, and the sum goes over all pairs of vertices. In this paper, we characterize the connected unicyclic graph with minimum Wiener indices among all connected unicyclic graphs of order n and girth g with k pendent vertices.