C₇-Decompositions of the Tensor Product of Complete Graphs

• Autorzy: R.S. Manikandan , P. Paulraja
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

cycle decomposition; tensor product

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 37
• Numer: 3
• Strony: 523-535

Daty

wydano

2017-08-01

otrzymano

2015-12-14

poprawiono

2016-05-05

zaakceptowano

2016-05-05

online

2017-07-06

Twórcy

autor

R.S. Manikandan

• , , -,

autor

P. Paulraja

• , , Krishnankoil-,

Identyfikatory

DOI

10.7151/dmgt.1936