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Small vertex-transitive and Cayley graphs of girth six and given degree: an algebraic approach

Loz, Eyal; Mačaj, Martin; Miller, Mirka; Šiagiová, Jana; Siran, Jozef and Tomanová, Jana (2011). Small vertex-transitive and Cayley graphs of girth six and given degree: an algebraic approach. Journal of Graph Theory, 68(4) pp. 265–284.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1002/jgt.20556
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Abstract

We examine the existing constructions of the smallest known vertex-transitive graphs of a given degree and girth 6. It turns out that most of these graphs can be described in terms of regular lifts of suitable quotient graphs. A further outcome of our analysis is a precise identification of which of these graphs are Cayley. We also investigate higher level of transitivity of the smallest known vertex-transitive graphs of a given degree and girth 6 and relate their constructions to near-difference sets.

Item Type: Journal Article
Copyright Holders: 2010 John Wiley & Sons, Ltd
ISSN: 1097-0118
Keywords: graph; girth; degree; cage
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 34910
Depositing User: Jozef Širáň
Date Deposited: 25 Oct 2012 10:53
Last Modified: 30 Nov 2012 10:40
URI: http://oro.open.ac.uk/id/eprint/34910
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