On Edge-Transitive Graphs of Square-Free Order
Keywords: Edge-transitive graph, Arc-transitive graph, Stabilizer, Quasiprimitive permutation group, Almost simple group
AbstractWe study the class of edge-transitive graphs of square-free order and valency at most $k$. It is shown that, except for a few special families of graphs, only finitely many members in this class are basic (namely, not a normal multicover of another member). Using this result, we determine the automorphism groups of locally primitive arc-transitive graphs with square-free order.