Classification of edge-transitive rose window graphs

✍ Scribed by István Kovács; Klavdija Kutnar; Dragan Marušič

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 177 KB
• Volume: 65
• Category: Article
• ISSN: 0364-9024
• DOI: 10.1002/jgt.20475

✦ Synopsis

Abstract

Given natural numbers n⩾3 and 1⩽a, r⩽n−1, the rose window graph R~n~(a, r) is a quartic graph with vertex set \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}${{{x}}_{{i}}|{{i}}\in {\mathbb{Z}}_{{n}}} \cup {{{y}}_{{i}}|{{i}}\in{\mathbb{Z}}_{{n}}}$\end{document} and edge set \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}${{{{x}}_{{i}},{{x}}_{{{i+1}}}} \mid {{i}}\in {\mathbb{Z}}_n } \cup {{{{y}}_{{{i}}},{{y}}_{{{i+r}}}}\mid {{i}} \in{\mathbb{Z}}_{{n}}}\cup {{{{x}}_{{{i}}},{{y}}_{{{i}}}} \mid {{i}}\in {\mathbb{Z}}_{{{n}}}}\cup {{{{x}}_{{{i+a}}},{{y}}_{{{i}}}} \mid{{i}} \in {\mathbb{Z}}_{{{n}}}}$\end{document}. In this article a complete classification of edge‐transitive rose window graphs is given, thus solving one of the three open problems about these graphs posed by Steve Wilson in 2001. © 2010 Wiley Periodicals, Inc. J Graph Theory 65: 216–231, 2010