Geodesic
C7-Decompositions of the Tensor Product of Complete Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 523-535

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In this paper we consider a decomposition of Km × Kn, where × denotes the tensor product of graphs, into cycles of length seven. We prove that for m, n ≥ 3, cycles of length seven decompose the graph Km × Kn if and only if (1) either m or n is odd and (2) 14 | m(m − 1)n(n − 1). The results of this paper together with the results of [Cp-Decompositions of some regular graphs, Discrete Math. 306 (2006) 429–451] and [C5-Decompositions of the tensor product of complete graphs, Australasian J. Combinatorics 37 (2007) 285–293], give necessary and sufficient conditions for the existence of a p-cycle decomposition, where p ≥ 5 is a prime number, of the graph Km × Kn.
Keywords: cycle decomposition, tensor product 
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     title = {C\protect\textsubscript{7}-Decompositions of the {Tensor} {Product} of {Complete} {Graphs}},
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Manikandan, R.S.; Paulraja, P. C7-Decompositions of the Tensor Product of Complete Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 523-535. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a1/