Small vertex-transitive graphs of given degree and girth

@article{Jajcay2011SmallVG,
  title={Small vertex-transitive graphs of given degree and girth},
  author={Robert Jajcay and Jozef Sir{\'a}n},
  journal={Ars Math. Contemp.},
  year={2011},
  volume={4},
  pages={375-384}
}
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… CONTINUE READING

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