C7-Decompositions of the Tensor Product of Complete Graphs

R.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 -