HARARY INDEX OF THE k-TH POWER OF A GRAPH

The k-th power of a graph G, denoted by G(k), is a graph with the same set of vertices as G, such that two vertices are adjacent in G(k) if and only if their distance in G is at most k. The Harary index H is the sum of the reciprocal distances of all pairs of vertices of the underlying graph. Lower and upper bounds on H(G(k)) are obtained. A Nordhaus Gaddum type inequality for H(G(k)) is also established.