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Commuting decompositions of complete graphs

✍ Scribed by Saieed Akbari; Allen Herman

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 129 KB
Volume: 15
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20112

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✦ Synopsis

Abstract

We say that two graphs G and H with the same vertex set commute if their adjacency matrices commute. In this article, we show that for any natural number r, the complete multigraph K is decomposable into commuting perfect matchings if and only if n is a 2‐power. Also, it is shown that the complete graph K~n~ is decomposable into commuting Hamilton cycles if and only if n is a prime number. © 2006 Wiley Periodicals, Inc. J Combin Designs

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