Half-arc-transitive graphs of order 4p of valency twice a prime

Xiuyun Wang, Yan-Quan Feng


A graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. Let p be a prime. Cheng and Oxley [On weakly symmetric graphs of order twice a prime, J. Combin. Theory B 42 (1987), 196−211] proved that there is no half-arc-transitive graph of order 2p, and Alspach and Xu [1/2-transitive graphs of order 3p, J. Algebraic Combin. 3 (1994), 347−355] classified half-arc-transitive graphs of order 3p. In this paper we classify half-arc-transitive graphs of order 4p of valency 2q for each prime q ≥ 5. It is shown that such graphs exist if and only if p − 1 is divisible by 4q. Moreover, for such p and q a unique half-arc-transitive graph of order 4p and valency 2q exists and this graph is a Cayley graph.


Cayley graph, half-arc-transitive graph, transitive graph

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DOI: https://doi.org/10.26493/1855-3974.125.164

ISSN: 1855-3974

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