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C7-Decompositions of the Tensor Product of Complete Graphs

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Manikandan R. S., Paulraja P.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 3

523-535

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Manikandan R. S.

1 Paulraja P.

1 2017

Wyniki wyszukiwania

C7-Decompositions of the Tensor Product of Complete Graphs