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

2016/05/26 by Wang, Yi, Feng, Yan-Quan
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1605.08123

Abstract

A graph is called \em 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 tetravalent half-arc-transitive graph of order p or p². Xu~[Half-transitive graphs of prime-cube order, J. Algebraic Combin. 1 (1992) 275-282] 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.

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