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Sibirskii Matematicheskii Zhurnal, 2007, Volume 48, Number 5, Pages 1142–1146
(Mi smj1796)
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This article is cited in 2 scientific papers (total in 2 papers)
Isomorphisms of Cayley graphs of a free Abelian group
A. A. Ryabchenko Moscow Institute of Physics and Technology
Abstract:
A group $G$ is called a $CI$-group provided that the existence of some automorphism $\sigma\in\operatorname{Aut}(G)$, such that $\sigma(A)=B$ follows from an isomorphism $\operatorname{Cay}(G,A)\cong\operatorname{Cay}(G,B)$ between Cayley graphs, where $A$ and $B$ are two systems of generators for $G$. We prove that every finitely generated abelian group is a $CI$-group.
Keywords:
abelian group, Cayley graph, distance graph.
Received: 05.09.2005
Citation:
A. A. Ryabchenko, “Isomorphisms of Cayley graphs of a free Abelian group”, Sibirsk. Mat. Zh., 48:5 (2007), 1142–1146; Siberian Math. J., 48:5 (2007), 919–922
Linking options:
https://www.mathnet.ru/eng/smj1796 https://www.mathnet.ru/eng/smj/v48/i5/p1142
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Abstract page: | 321 | Full-text PDF : | 128 | References: | 33 |
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