Eccentric Connectivity Index, Hyper and Reverse-Wiener Indices of the Subdivision Graph

If G is a connected graph with vertex set V, then the eccentric connectivity index of G, \xi^{(c)}(G) is defined as Σ deg(v). ec(v)$ where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. The Wiener index W(G)= 1/2 [Σ d(u,v)], the hyper-Wiener index WW(G) = 1/2 [Σ d(u,v) + Σ d^ 2(u,v)] and the reverse-Wiener index ʌ (G) = \frac{n(n-1)D}{2} -W(G) , where d(u,v) is the distance of two vertices u, v in G, d^ 2 (u,v) = d(u,v)^ 2 , n =|V(G)| and D is the diameter of G. In this paper, we determine the eccentric connectivity index of the subdivision graph of the complete graphs, tadpole graphs and the wheel graphs. Also, derive an expressions for the hyper and reverse-Wiener indices of the same class of graphs.