Half-arc-transitive graphs of prime-cube order of small valencies

Yi Wang, Yan-Quan Feng


A graph is called half-arc-transitive if its full automorphism group acts transitively on vertices and edges, but not on arcs. It is well known that for any prime p there is no half-arc-transitive graph of order p or p2. In 1992, Xu classified half-arc-transitive graphs of order p3 and valency 4. In this paper we classify half-arc-transitive graphs of order p3 and valency 6 or 8. In particular, the first known infinite family of half-arc-transitive Cayley graphs on non-metacyclic p-groups is constructed.


Cayley graph, half-arc-transitive graph, automorphism group

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ISSN: 1855-3974

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