Small vertex-transitive and cayley graphs of girth six and given degree: An algebraic approach

摘要

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.