2016/03/04 by Giudici, Michael, Kovács, István, Li, Cai Heng +1
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1603.01368
For an integer k≥ 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.