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Isomorphic Cayley graphs on nonisomorphic groups

✍ Scribed by Morris, Joy


Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
349 KB
Volume
31
Category
Article
ISSN
0364-9024

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✦ Synopsis


The issue of when two Cayley digraphs on different abelian groups of prime power order can be isomorphic is examined. This had previously been determined by Anne Joseph for squares of primes; her results are extended.


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Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T βŠ‚ G, Cay(G, S) ∼ = Cay(G, T ) implies S Ξ± = T for some Ξ± ∈ Aut(G), then Cay(G, S) is called a CI-graph of G. For a group G, if all Cayley digraphs of valency m are CI-graphs, then G is said to have the m-DCI property;