On isomorphisms of connected Cayley graphs
نویسندگان
چکیده
منابع مشابه
Isomorphisms of Cayley graphs on nilpotent groups
Let S be a finite generating set of a torsion-free, nilpotent group G. We show that every automorphism of the Cayley graph Cay(G;S) is affine. (That is, every automorphism of the graph is obtained by composing a group automorphism with multiplication by an element of the group.) More generally, we show that if Cay(G1;S1) and Cay(G2;S2) are connected Cayley graphs of finite valency on two nilpot...
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A Cayley graph Cay(G, S) of a group G is called a CI-graph if whenever T is another subset of G for which Cay(G, S) ∼= Cay(G, T ), there exists an automorphism σ of G such that Sσ = T . For a positive integer m, the group G is said to have the m-CI property if all Cayley graphs of G of valency m are CI-graphs; further, if G has the k-CI property for all k ≤ m, then G is called an m-CI-group, an...
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We refer to the preceding theorem as the Chen–Quimpo theorem throughout the paper. Are there other families of groups which admit analogues of the Chen–Quimpo theorem? A natural direction in which to look is towards groups that are, in some sense, ‘almost’ abelian. The dihedral groups have been investigated [2]. Another family of groups, and the subject of this paper, is the family of Hamiltoni...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)81821-3