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s-Regular cubic graphs as coverings of the complete bipartite graph K3,3

✍ Scribed by Yan-Quan Feng; Jin Ho Kwak

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 138 KB
Volume: 45
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10151

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✦ Synopsis

Abstract

A graph is s‐regular if its automorphism group acts freely and transitively on the set of s‐arcs. An infinite family of cubic 1‐regular graphs was constructed in [10], as cyclic coverings of the three‐dimensional Hypercube. In this paper, we classify the s‐regular cyclic coverings of the complete bipartite graph K~3,3~ for each ≥ 1 whose fibre‐preserving automorphism subgroups act arc‐transitively. As a result, a new infinite family of cubic 1‐regular graphs is constructed. © 2003 Wiley Periodicals, Inc. J Graph Theory 45: 101–112, 2004

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