On positive and negative atoms of Cayley digraphs
β Scribed by Gilles Zemor
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 172 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0166-218X
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π SIMILAR VOLUMES
A necessary and sufficient condition is given for two Cayley digraphs X 1 = Cay(G 1 , S 1 ) and X 2 = Cay(G 2 , S 2 ) to be isomorphic, where the groups G i are nonisomorphic abelian 2-groups, and the digraphs X i have a regular cyclic group of automorphisms. Our result extends that of Morris [J Gra
## Abstract We find all possible lengths of circuits in Cayley digraphs of twoβgenerated abelian groups over the twoβelement generating sets and over certain threeβelement generating sets.
Let G be finite group and let S be a subset of G. We prove a necessary and sufficient condition for the Cayley digraph Xc~,s) to be primitive when S contains the central elements of G. As an immediate consequence we obtain that a Cayley digraph X 1, (6 S) on an Abelian group is primitive if and only
## Abstract Let __Z__~__p__~ denote the cyclic group of order __p__ where __p__ is a prime number. Let __X__ = __X__(__Z__~__p__~, __H__) denote the Cayley digraph of __Z__~__p__~ with respect to the symbol __H__. We obtain a necessary and sufficient condition on __H__ so that the complete graph on
Given any prime p, there are two non-isomorphic groups of order p2. We determine precisely when a Cayley digraph on one of these groups is isomorphic to a Cayley digraph on the other group, Namely, let X = Cay(G: T) be a Cayley digraph on a group G of order p2 with generating set T. We prove that X