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2-valent Cayley digraphs over nonabelian groups. (Chinese. English summary) Zbl 1474.05165

Summary: We called a Cayley digraph \(X = {\mathrm{Cay}} (G, S)\) normal if the right regular representation \(R(G)\) of G is normal in the full automorphism group \({\mathrm{Aut}} (X)\) of \(X\). The sufficient conditions for the 2-valent Cayley digraphs of nonabelian groups to be normal are given. In addition, 2-valent normal Cayley digraphs on generalized quaternion groups are determined by means of automorphism groups and checking the cycles.

MSC:

05C20 Directed graphs (digraphs), tournaments
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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