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Harary index of the k-th power of a graph

Su Guifu (Beijing Institute of Technology, Beijing, P.R. China)
Xiong Liming (Beijing Institute of Technology, Beijing, P.R. China)
Gutman Ivan (Faculty of Science, Kragujevac)

The k-th power of a graph G, denoted by Gk, is a graph with the same set of vertices as G, such that two vertices are adjacent in Gk 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(Gk) are obtained. A Nordhaus-Gaddum type inequality for H(Gk) is also established.

Keywords: Harary index, k-th power of graph, Nodrhaus-Gaddum type inequality