Normal edge-transitive and -arc-transitive semi-Cayley graphs

ABSTRACT

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 $\frac{1}{2}$-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 $\frac{1}{2}$-arc-transitive semi-Cayley will be presented.

KEYWORDS:

• Normal arc-transitive
• normal edge-transitive
• semi-Cayley graph

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D60
• 05B25