Geodesic
Harary Index of Product Graphs
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 17-33.

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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 × K_m_0,m_1,...,m_r−1 and the strong product G⊠K_m_0,m_1,...,m_r−1, where K_m_0,m_1,...,m_r−1 is the complete multipartite graph with partite sets of sizes m_0,m_1, . . .,m_r−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 ○ G′ is obtained.
Keywords: tensor product, strong product, wreath product, Harary index 
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Pattabiraman, K.; Paulraja, P. Harary Index of Product Graphs. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 17-33. http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a1/

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