Automorphism groups and isomorphisms of Cayley digraphs of Abelian groups.
Automorphism groups and isomorphisms of Cayley digraphs of Abelian groups.
The authors prove that if \(S\) is a minimal generating set of a finite Abelian group \(G\) and the Sylow 2-subgroup of \(G\) is cyclic, then \(S\) and \(S\cup S^{-1}\) are CI-subsets and the corresponding Cayley digraph and graph are normal in the sense that the right regular representation of \(G\) is normal in the group of automorphisms of the graph. This answers in the affirmative a special case of a question raised by Xu: Problem 6 in \textit{M. Xu} [Automorphism groups and isomorphisms of Cayley digraphs, Discrete Math. 182, No. 1-3, 309-319 (1998; Zbl 0887.05025)].
Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), Sylow 2-subgroup, CI-subsets, Cayley digraph, group of automorphisms, Graphs and abstract algebra (groups, rings, fields, etc.)
Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), Sylow 2-subgroup, CI-subsets, Cayley digraph, group of automorphisms, Graphs and abstract algebra (groups, rings, fields, etc.)
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