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
Circuits in cayley digraphs of finite abelian groups
β Scribed by Anne Marie Wilkinson
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 290 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
Let G be a finite group, S a subset of G" [1], and let Cay(G, S ) denote the Cayley digraph of G with respect to S. If, for all subsets S, T of G"[1] of size at most m, Cay(G, S )$Cay(G, T) implies that S \_ =T for some \_ # Aut(G), then G is called an m-DCI-group. In this paper, we prove that, for
For a finite group G and a subset S of G which does not contain the identity of G, denote by Cay(G, S) the Cayley digraph of G with respect to S. An automorphism \_ of the group G induces a graph isomorphism from Cay(G, S) to Cay(G, S \_ ). In this paper, we investigate groups G and Cayley digraphs
Let G be a finite group, S a subset of G=f1g; and let Cay Γ°G; SΓ denote the Cayley digraph of G with respect to S: If, for any subset T of G=f1g; CayΓ°G; SΓ ffi CayΓ°G; T Γ implies that S a ΒΌ T for some a 2 AutΓ°GΓ; then S is called a CI-subset. The group G is called a CIM-group if for any minimal gene
Alspach has conjectured that any 2k-regular connected Cayley graph cay(A, S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In this paper, the conjecture is shown to be true if S=[s 1 , s 2 , ..., s k ] is a minimal generating set of an abelian group A of odd order (where a