# C7-Decompositions of the Tensor Product of Complete Graphs

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 3, page 523-535
- ISSN: 2083-5892

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topR.S. Manikandan, and P. Paulraja. "C7-Decompositions of the Tensor Product of Complete Graphs." Discussiones Mathematicae Graph Theory 37.3 (2017): 523-535. <http://eudml.org/doc/288567>.

@article{R2017,

abstract = {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.},

author = {R.S. Manikandan, P. Paulraja},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {cycle decomposition; tensor product},

language = {eng},

number = {3},

pages = {523-535},

title = {C7-Decompositions of the Tensor Product of Complete Graphs},

url = {http://eudml.org/doc/288567},

volume = {37},

year = {2017},

}

TY - JOUR

AU - R.S. Manikandan

AU - P. Paulraja

TI - C7-Decompositions of the Tensor Product of Complete Graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2017

VL - 37

IS - 3

SP - 523

EP - 535

AB - 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.

LA - eng

KW - cycle decomposition; tensor product

UR - http://eudml.org/doc/288567

ER -

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