Hosoya Polynomial of Jahangir graphs J4,m

Let G be a simple graph. The Hosoya polynomial of G is H(G,x)= where d(u,v) denotes the distance between vertices u and v. And the Wiener index is the sum of distances between all pairs of vertices of a connected graph G as W(G)= In this paper we compute the Hosoya polynomial for Jahangir graph J4,m. As a consequence we obtain the Wiener index of this graph