On arc-transitive pentavalent graphs of order 2mpn

摘要

A graph Γ is symmetric or arc-transitive if its automorphism group Aut(Γ) is transitive on the arc set of the graph. Let p be an odd prime. Pentavalent symmetric graphs of order 2pn with n ≥ 2 have been considered by Pan et al. in [Algebra Colloq. 22 (2015) 383-394] and by Feng et al. in [Discrete Math. 339 (2016) 2640-2651]. This paper gives a depiction of pentavalent symmetric graphs of order 2mpn for any integers m ≥ 2 and n ≥ 1. As an application, connected pentavalent symmetric graphs of order 16p, 8p2 and 8p3 are classified.