The Cayley Isomorphism Property for Cayley Maps
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چکیده
منابع مشابه
The Cayley Isomorphism Property for Cayley Maps
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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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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Skoviera, M. and J. ‘&Iii, Regular maps from Cayley graphs, Part i: Balanced Cayley maps, Discrete Mathematics IO9 (1992) 265-276. A Cayley map is a Cayley graph 2-cell embedded in some orientable surface so that the local rotations at every vertex are identical. Two types of Cayley maps are introduced: the balanced and antibalanced Cayley maps. In Part 1, conditions are given uuder which a bal...
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The Cayley map for the rotation group SO(3) is extended to a map from the Lie algebra of the group of rigid body motions SE(3) to the group itself. This is done in several inequivalent ways. A close connection between these maps and linear line complexes associated with a finite screw motions is found.
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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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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/5962