Harary index of product graphs

Abstract

The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, the exact formulae for the Harary indices of tensor product G ×Km0,m1,.,mr-1 and the strong product G Km0,m1,.,mr-1, where Km0,m1,.,mr-1 is the complete multipartite graph with partite sets of sizes m0,m1,. ,mr-1 are obtained. Also upper bounds for the Harary indices of tensor and strong products of graphs are estabilished. Finally, the exact formula for the Harary index of the wreath product G o G′ is obtained.