Constructing an infinite family of cubic 1-regular graphs
type: Item
instance of: scholarly article
title: Constructing an infinite family of cubic 1-regular graphs
zbMATH Open document ID: 1016.05039
published in: European Journal of Combinatorics
publication date: 2003-03-18T00:00:00Z
review text: An arc in a graph is an edge fixed with one of the two directions. A graph is 1-regular if there is an automorphism that carries any arc to any other arc. In this paper, the authors construct an infinite family of cubic 1-regular graphs of order \(8(k^2 + k + 1)\), where \(k \geq 2\). It was known that there were cubic 1-regular graphs of order \(2n\), when \(n \geq 13\) is odd and 3 divides \(\phi (n)\) (\(\phi\) denotes the Euler phi function). The authors show that their new class is different from this known class. Their graphs are constructed using cyclic-covering graphs of the 3-dimensional cube.
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1884143
author: Yan-Quan Feng
author: Jin Ho Kwak
reviewed by: Dan S. Archdeacon
MaRDI profile type: Publication
full work available at URL: eujc.2002.0589
OpenAlex ID: W2036738625
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DOI: 10.1006/EUJC.2002.0589
description: scientific article; zbMATH DE number 1884143