Cubic Semisymmetric Graphs of Order 2 qp 2

A regular edge-transitive graph is said to be semisymmetric if it is not vertex-transitive. Let p be a prime. By Folkman [J. Combin. Theory 3 (1967), 215–232], there is no cubic semisymmetric graph of order 2p or 2p2, and by Hua et al. [Science in China A 54 (2011), 1937–1949], there is no cubic semisymmetric graph of order 4p2. Lu et al. [Science in China A 47 (2004), 11–17] classified connected cubic semisymmetric graphs of order 6p2. In this paper, for p > q ≥ 5 two distinct odd primes, it is shown that the sufficient and necessary conditions which a connected cubic edge transitive bipartite graph of order 2qp2 is semisymmetric.