Hamiltonian decompositions of Cayley graphs on Abelian groups
type: Item
instance of: scholarly article
title: Hamiltonian decompositions of Cayley graphs on Abelian groups
zbMATH Open document ID: 0809.05058
DOI: 10.1016/0012-365X(94)90381-6
author: Jiuqiang Liu
published in: Discrete Mathematics
publication date: 1995-03-20T00:00:00Z
review text: The author considers when the Cayley graph \(\text{cay}(A,S)\), where \((A,+)\) is a group, \(A\) denotes the vertex set and \(S\subseteq A\), \(0\not\in S\), determines the edges of the graph (\(xy\) is an edge if and only if \(x- y\in S\cup- S\)), has a Hamilton decomposition. It is shown that such a decomposition exists: (1) if \(S= \{s_ 1,\dots, s_ k\}\) is a generating set of \(A\) such that \(\text{gcd}(\text{ord}(s_ i), \text{ord}(s_ j))= 1\) for \(i\neq j\), or a minimal generating set of \(A\) with \(k= 3\) and with either two elements of order 2 or one element of prime order; and (2) if \(A\) is an Abelian group of odd order and \(S= \{s_ 1,s_ 2,s_ 3\}\) is a minimal generating set of \(A\).
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 626346
zbMATH Keywords: Cayley graph
zbMATH Keywords: Hamilton decomposition
zbMATH Keywords: generating set
zbMATH Keywords: Abelian group
reviewed by: Katherine Heinrich
MaRDI profile type: Publication
cites work: Q3197858
cites work: Décomposition de la somme cartesienne d'un cycle et de l'union de deux cycles hamiltoniens en cycles hamiltoniens
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cites work: Q3158579
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cites work: Hamiltonian circuits in Cayley graphs
full work available at URL: 0012-365x(94)90381-6
OpenAlex ID: W2042747061
description: scientific article; zbMATH DE number 626346