Abstract

A graph $\Gamma$ is called a semi-Cayley graph over a group $G$, if there 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 all non-normal bicirculants over a group of prime order.

Keywords: Semi-Cayley graph; bicirculant; normal semi-Cayley graph.

MSC: 05C25, 20B25

Pages:  338$-$343     

Volume  70 ,  Issue  4 ,  2018