Geodesic
Tetravalent half-arc-transitive graphs of order $2pq$
Journal of Algebraic Combinatorics, Tome 33 (2011) no. 4, pp. 543-553.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A graph is $half-arc-transitive$ if its automorphism group acts transitively on its vertex set, edge set, but not arc set. Let $p$ and $q$ be primes. It is known that no tetravalent half-arc-transitive graphs of order $2 p ^{2}$ exist and a tetravalent half-arc-transitive graph of order $4 p$ must be non-Cayley; such a non-Cayley graph exists if and only if $p - 1$ is divisible by 8 and it is unique for a given order. Based on the constructions of tetravalent half-arc-transitive graphs given by Marušič (J. Comb. Theory B 73:41-76, 1998), in this paper the connected tetravalent half-arc-transitive graphs of order $2 pq$ are classified for distinct odd primes $p$ and $q$.
Keywords: keywords Cayley graph, vertex-transitive graph, half-arc-transitive graph 
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     title = {Tetravalent half-arc-transitive graphs of order $2pq$},
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Feng, Yan-Quan; Kwak, Jin Ho; Wang, Xiuyun; Zhou, Jin-Xin. Tetravalent half-arc-transitive graphs of order $2pq$. Journal of Algebraic Combinatorics, Tome 33 (2011) no. 4, pp. 543-553. http://geodesic.mathdoc.fr/item/JAC_2011__33_4_a3/