On Edge-Transitive Graphs of Square-Free Order

Cai Heng Li, Zai Ping Lu, Gai Xia Wang


We 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.


Edge-transitive graph; Arc-transitive graph; Stabilizer; Quasiprimitive permutation group; Almost simple group

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