Abstract
For an integer k⩾1, a graph is called a k-multicirculant if its automorphism group contains a cyclic semiregular subgroup with k orbits on the vertices. If k is even, there exist infinitely many cubic arc-transitive k-multicirculants. We conjecture that, if k is odd, then a cubic arc-transitive k-multicirculant has order at most 6k2. Our main result is a proof of this conjecture when k is squarefree and coprime to 6.
Original language | English |
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Pages (from-to) | 80-94 |
Number of pages | 15 |
Journal | Journal of Combinatorial Theory. Series B |
Volume | 125 |
DOIs | |
Publication status | Published - 1 Jul 2017 |