Arc-transitive Pentavalent Graphs of Order 4pq

Abstract

This  paper determines all arc-transitive pentavalent graphs of order $4pq$, where $p,q\ge 5$ are distinct primes. The cases $q=1,2,3$ and $q=p$ is a prime have been treated previously by Hua et al. [Pentavalent symmetric graphs of order $2pq$, Discrete Math. 311 (2011), 2259-2267], Hua and Feng [Pentavalent symmetric graphs of order $8p$, J. Beijing Jiaotong University 35 (2011), 132-135], Guo et al. [Pentavalent symmetric graphs of order $12p$, Electronic J. Combin. 18 (2011), #P233] and Huang et al. [Pentavalent symmetric graphs of order four time a prime power, submitted for publication], respectively.