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Li, Cai Heng; Lu, Zai Ping; Wang, Gai Xia

On edge-transitive graphs of square-free order. (English) Zbl 1327.05146

Electron. J. Comb. 22, No. 3, Research Paper P3.25, 22 p. (2015).
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.

Cited in 8 Documents

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 group
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References:

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