On Wiener polarity index of cactus graphs
  The Wiener polarity index of a graph G is the number of unordered pairs of vertices u, v such that the distance between u and v is 3. In this paper we give an explicit formula for the Wiener polarity index of cactus graphs. We also deduce formulas for some special cactus graphs. 
Nan Chen, Wen-Xue Du, Yi-Zheng Fan
math.CO