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Cubic arc-transitive $k$-circulants (1603.01368v1)
Published 4 Mar 2016 in math.CO and math.GR
Abstract: For an integer $k\geq 1$, a graph is called a $k$-circulant if its automorphism group contains a cyclic semiregular subgroup with $k$ orbits on the vertices. We show that, if $k$ is even, there exist infinitely many cubic arc-transitive $k$-circulants. We conjecture that, if $k$ is odd, then a cubic arc-transitive $k$-circulant has order at most $6k2$. Our main result is a proof of this conjecture when $k$ is squarefree and coprime to $6$.