On Edge-Primitive Graphs of Order as a Product of Two Distinct Primes

Abstract

A graph is edge-primitive if its automorphism group acts primitively on the edge set of the graph. Edge-primitive graphs form an important subclass of symmetric graphs. In this paper, edge-primitive graphs of order as a product of two distinct primes are completely determined. This depends on non-abelian simple groups with a subgroup of index pq being classified, where p>q are odd primes.

Keywords

• edge-primitive graphs
• primitive permutation group
• symmetric graphs