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One of the most widely known topological descriptors is the Wiener index or (Wiener number) named after American chemist Harold Wiener in 1947. Wiener number of a connected graph G is defined as the sum of the distances between distinct pairs of vertices of G..It correlates between physicochemical and structural properties.The hyper wiener index denoted by WW of a graph G was introduced by Randic and his definition is applicable to trees only. Klein, Lukovits and Gutman introduced the formula for both trees and cycle containing structures. The Hyper Wiener index is defined as WW (G) = (∑d(u ,v)+∑d(u,v))/2, where d(u,v) denotes the distance between the vertices u and v in the graph G and the summations run over all distinct pairs of vertices of G. Recently an edge version of Hyper Wiener Index was introduced by Ali Iranmanesh.In this paper, we have determined Hyper Wiener numbers of some Cluster graphs and also for some bipartite cluster graphs

Vertex and Edge Hyper Wiener Number of Some Cluster Graphs