On edge-transitive graphs of square-free order. (English) Zbl 1327.05146
Summary: 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.
MSC:
05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
20B25 | Finite automorphism groups of algebraic, geometric, or combinatorial structures |
Keywords:
edge-transitive graph; arc-transitive graph; stabilizer; quasiprimitive permutation group; almost simple groupReferences:
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