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Groups of automorphisms of finite regular cubic graphs. (English. Russian original) Zbl 0742.05046

Sib. Math. J. 30, No. 6, 925-935 (1989); translation from Sib. Mat. Zh. 30, No. 6(178), 110-121 (1989).
Connected nonoriented graphs without loops are considered. A graph is called a regular cubic one if every vertex has degree 3 and the automorphism group acts transitively on the set of ordered pairs of adjacent vertices. The main result presented in the paper is the following. For \(n\neq 10\) any automorphism group of a regular cubic graph with \(2(n-1)\) vertices is imbedded in one of the groups \(\text{Aut }F_ n\) or \(S_ 2\times S_{n+1}\).

MSC:

05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
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References:

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