Bipartite edge-transitive bi-p-metacirculants

Yan-Quan Feng, Yi Wang

Abstract


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.


Keywords


Bi-Cayley graph, half-arc-transitive graph, metacyclic group

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DOI: https://doi.org/10.26493/1855-3974.1801.eb1

ISSN: 1855-3974

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