Reciprocal degree distance of product graphs

The reciprocal degree distance (RDD  ), defined for a connected graph GG as vertex-degree-weighted sum of the reciprocal distances, that is, RDD(G)=∑u,v∈V(G)(d(u)+d(v))dG(u,v). The reciprocal degree distance is a weight version of the Harary index, just as the degree distance is a weight version of the Wiener index. In this paper, the exact formulae for the reciprocal degree distance 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. Finally, we apply our result to compute the reciprocal degree distance of open fence and closed fence graphs.