On automorphism groups of symmetric Cayley graphs of finite simple groups with valency six. (English) Zbl 1179.05051
Summary: We investigate the full automorphism groups of six-valent symmetric Cayley graphs \(\Gamma = \text{Cay}(G,S)\) for finite non-abelian simple groups \(G\). We prove that for most finite non-abelian simple groups \(G\), if \(\Gamma \) contains no cycle of length 4, then \(\text{Aut}\Gamma = G \cdot \text{Aut}(G,S)\), where \(\text{Aut}(G,S) \leq S _{6}\).
MSC:
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 20B25 | Finite automorphism groups of algebraic, geometric, or combinatorial structures |
References:
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