On the generalized Wiener polarity index for some classes of graphs

The generalized Wiener polarity index W{ink}(G) of a graph G = (V, E) is defined as a number of unordered pairs {u, v} of G such that the shortest distance between u and v is equal to k: W_k(G) = |{{u, v}, d(u, v) = k, u, v ∈ V (G)}| In this paper we give some results for 2-trees in case of mentioned index. We present an infinite family of 2-trees with maximum value of generalized Wiener polarity index.