THE HYPER-WIENER INDEX OF THE κth POWER OF A GRAPH

The kth power of a graph G, denoted by G(k), is a graph whose vertex set is V (G), two distinct vertices being adjacent in Gk if and only if their distance in G is at most k. The hyper-Wiener index WW(G) of a graph G is defined as WW(G) = (1/2) Sigma({u, v}subset of V (G))(d(G)(u, v) + d(G)(2) (u, v)), where d(G)(u, v) is the distance between vertices u and v in G. In this paper, the bounds on the hyper-Wiener index of the graph G(k) are given. The Nordhaus-Gaddum-type inequality for the hyper-Wiener-index of the graph G(k) is also presented.