Jajcay, Robert and Širáň, Jozef
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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|
|Keywords:||vertex-transitive graph; cage; degree; girth|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics|
|Depositing User:||Jozef Širáň|
|Date Deposited:||09 Dec 2011 10:27|
|Last Modified:||01 Dec 2012 05:57|
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