A Cayley digraph X = Cay(G, S) is said to be normal for G if the regular representation R(G) of G is normal in the full automorphism group Aut(X ) of X . A characterization of normal minimal Cayley digraphs for abelian groups is given. In addition, the abelian groups, all of whose minimal Cayley dig
Vosperian and superconnected Abelian Cayley digraphs
β Scribed by Y. O. Hamidoune; A. S. Llado; O. Serra
- Publisher
- Springer Japan
- Year
- 1991
- Tongue
- English
- Weight
- 591 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
## 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.
We show every finitely-generated, infinite abeliar\_ group (i.e. Zn x G where G is a finite abelian group) has a minimal generating set for which the Cayley digraph has a two-way in&rite hamiltonian path, and if n 2 2, then this Cayley digraph also has a one-way infinite hamiltonian path. We show fu
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