Loz, Eyal; Mačaj, Martin; Miller, Mirka; Šiagiová, Jana; Siran, Jozef and Tomanová, Jana
Small vertex-transitive and Cayley graphs of girth six and given degree: an algebraic approach.
Journal of Graph Theory, 68(4) pp. 265–284.
We examine the existing constructions of the smallest known vertex-transitive graphs of a given degree and girth 6. It turns out that most of these graphs can be described in terms of regular lifts of suitable quotient graphs. A further outcome of our analysis is a precise identification of which of these graphs are Cayley. We also investigate higher level of transitivity of the smallest known vertex-transitive graphs of a given degree and girth 6 and relate their constructions to near-difference sets.
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