Geodesic
Half-arc-transitive graphs of order 4p of valency twice a prime
Ars Mathematica Contemporanea, Tome 3 (2010) no. 2, pp. 151-163.

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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.
DOI : 10.26493/1855-3974.125.164
Keywords: Cayley graph, half-arc-transitive graph, transitive graph 
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Xiuyun Wang; Yan-Quan Feng. Half-arc-transitive graphs of order 4p of valency twice a prime. Ars Mathematica Contemporanea, Tome 3 (2010) no. 2, pp. 151-163. doi : 10.26493/1855-3974.125.164. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.125.164/

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