The maximum Wiener polarity index of unicyclic graphs

The Wiener polarity index of a graph G   is the number of unordered pairs of vertices u,vu,v such that the distance between u and v is 3. In this paper, we obtain a upper bound for the Wiener polarity index of unicyclic chemical graphs. Moreover, the maximum Wiener polarity index of unicyclic graphs is determined, and the corresponding extremal graphs are characterized.