Normal edge-transitive and 1/2-arc-transitive semi-Cayley graphs

摘要

A graph is said to be a semi-Cayley graph over a group G if it admits G as a semiregular automorphism group with two orbits of equal size. In this paper, definition of normal edge-transitive, arc-transitive and 1/2-arc-transitive semi-Cayley graphs are given. The main properties of such semi-Cayley graphs are shown and a condition for a graph to be a normal edge-transitive, arc-transitive, or 1/2-arc-transitive semi-Cayley will be presented.