New families of small regular graphs of girth 5
Abstract
In this paper we are interested in the Cage Problem that consists in constructing regular graphs of given girth g and minimum order. We focus on girth g=5, where cages are known only for degrees k 7. We construct regular graphs of girth 5 using techniques exposed by Funk [Note di Matematica. 29 suppl.1, (2009) 91 - 114] and Abreu et al. [Discrete Math. 312 (2012), 2832 - 2842] to obtain the best upper bounds known hitherto. The tables given in the introduction show the improvements obtained with our results.
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