Geodesic
Small vertex-transitive graphs of given degree and girth
Ars Mathematica Contemporanea, Tome 4 (2011) no. 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 pairof parameters k ≥ 2 and g ≥ 3, improve the lower bounds on the order of the smallest (k, g) vertex-transitive graphs forcertain 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.
DOI : 10.26493/1855-3974.124.06d
Keywords: vertex-transitive graph, cage, degree, girth 
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Robert Jajcay; Jozef Širáň. Small vertex-transitive graphs of given degree and girth. Ars Mathematica Contemporanea, Tome 4 (2011) no. 2, pp. 375-384. doi : 10.26493/1855-3974.124.06d. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.124.06d/

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