منابع مشابه
The isomorphism problem for Cayley graphs
The isomorphism problem for Cayley graphs over a group H will be considered and solved completely for cyclic groups H of prime power order for every prime p including p = 2. The method we use to obtain our solution is based on Schur rings. This method can be applied as well to colored Cayley graphs, and its scope admits further generalizations. 1. How to solve the isomorphism problem? In this p...
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We give a necessary condition to reduce the Cayley isomorphism problem for Cayley objects of a nilpotent or abelian group G whose order satisfies certain arithmetic properties to the Cayley isomorphism problem of Cayley objects of the Sylow subgroups of G in the case of nilpotent groups, and in the case of abelian groups to certain natural subgroups. As an application of this result, we show th...
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The Cayley Isomorphism property for combinatorial objects was introduced by L. Babai in 1977. Since then it has been intensively studied for binary relational structures: graphs, digraphs, colored graphs etc. In this paper we study this property for oriented Cayley maps. A Cayley map is a Cayley graph provided by a cyclic rotation of its connection set. If the underlying graph is connected, the...
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In this paper we are mainly concerned with the Cayley isomorphism problem for groups containing Q8. We prove that the group Q8 × C3 is not a CI-group with respect to colour ternary relational structures. Further, we prove that the non-nilpotent group C3 nQ8 is not a CI-group with respect to graphs.
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For a subset S of a group G such that 1 / ∈ S and S = S−1, the associated Cayley graph Cay(G, S) is the graph with vertex set G such that {x, y} is an edge if and only if yx−1 ∈ S. Each σ ∈ Aut(G) induces an isomorphism from Cay(G, S) to the Cayley graph Cay(G, Sσ ). For a positive integer m, the group G is called an m-CI-group if, for all Cayley subsets S of size at most m, whenever Cay(G, S) ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00164-9