Geodesic
Bipartite edge-transitive bi-p-metacirculants
Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 591-615.

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A graph is a bi-Cayley graph over a group if the group acts semiregularly on the vertex set of the graph with two orbits. Let G be a non-abelian metacyclic p-group for an odd prime p. In this paper, we prove that if G is a Sylow p-subgroup in the full automorphism group Aut(Γ) of a graph Γ, then G is normal in Aut(Γ). As an application, we classify the half-arc-transitive bipartite bi-Cayley graphs over G of valency less than 2p, while the case for valency 4 was given by Zhang and Zhou in 2019. It is further shown that there are no semisymmetric or arc-transitive bipartite bi-Cayley graphs over G of valency less than p.
DOI : 10.26493/1855-3974.1801.eb1
Keywords: Bi-Cayley graph, half-arc-transitive graph, metacyclic group 
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Yan-Quan Feng; Yi Wang. Bipartite edge-transitive bi-p-metacirculants. Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 591-615. doi : 10.26493/1855-3974.1801.eb1. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1801.eb1/

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