2019/10/11 by Liao, Hong Ci, Li, Jing Jian, Lu, Zai Ping
#05C25 #20B25 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1910.04931
A graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let Γ be a connected graph of odd order and twice prime valency, and let G be a subgroup of the automorphism group of \Ga. In the case where G acts transitively on the edges and quasiprimitively on the vertices of \Ga, we prove that either G is almost simple or G is a primitive group of affine type. If further G is an almost simple primitive group then, with two exceptions, the socle of G acts transitively on the edges of Γ.