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Small vertex-transitive graphs of given degree and girth

Jajcay, Robert and Širáň, Jozef (2011). Small vertex-transitive graphs of given degree and girth. Ars Mathematica Contemporanea, 4(2) pp. 375–384.

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We investigate the basic interplay between the small k-valent vertex-transitive graphs of girth g and the (k; g)-cages, the smallest k-valent graphs of girth g. We prove the existence of k-valent Cayley graphs of girth g for every pair of parameters k > 2 and g > 3,improve the lower bounds on the order of the smallest (k; g) vertex-transitive graphs for certain families with prime power girth, and generalize the construction of Bray, Parker and Rowley that has yielded several of the smallest known (k; g)-graphs.

Item Type: Journal Article
Copyright Holders: 2011 DMFA Slovenije
ISSN: 1855-3974
Keywords: vertex-transitive graph; cage; degree; girth
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 30422
Depositing User: Jozef Širáň
Date Deposited: 09 Dec 2011 10:27
Last Modified: 01 Dec 2012 05:57
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