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.
@article{bwmeta1.element.doi-10_7151_dmgt_1936,
author = {R.S. Manikandan and P. Paulraja},
title = {C7-Decompositions of the Tensor Product of Complete Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {37},
year = {2017},
pages = {523-535},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1936}
}
R.S. Manikandan; P. Paulraja. C7-Decompositions of the Tensor Product of Complete Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) pp. 523-535. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1936/