Non-normal $p$-bicirculants, $p$ a prime

Abstract

A graph $\Gamma$ is called a semi-Cayley graph over a group $G$, ifthere exists a semiregular subgroup $R_G$ of $Aut(\Gamma)$ isomorphic to $G$ with two orbits (of equal size).We say that $\Gamma$ is normal if $R_G$ is a normal subgroup of $Aut(\Gamma)$.Semi-Cayley graphs over cyclic groups are called bicirculants. In this paper, we determine allnon-normal bicirculants over a group of prime order.