Normal Cayley digraphs of cyclic groups with CI-property

On endo-Cayley digraphs: The hamiltonian property

Given a finite abelian group A, a subset ⊆ A and an endomorphism of A, the endo-Cayley digraph GA( , ) is defined by taking A as the vertex set and making every vertex x adjacent to the vertices (x)+ a with a ∈ . When A is cyclic and the set is of the form = {e, e + h, . . . , e + (d − 1)h}, the digraph G is called a consecutive digraph. In this paper we study the hamiltonicity of endo-Cayley d...

Automorphism groups of Cayley digraphs of Zp

We calculate the full automorphism group of Cayley digraphs of Zp, p an odd prime, as well as determine the 2-closed subgroups of Sm ≀ Sp with the product action.

Automorphism groups and isomorphisms of Cayley digraphs

Automorphism groups and isomorphisms of Cayley digraphs of Abelian groups

Let S be a minimal generating subset of the finite abelian group G. We prove that if the Sylow 2-subgroup of G is cyclic, then Sand S U S-l are CI-subsets and the corresponding Cayley digraph and graph are normal. Let G be a finite group and let S be a subset of G not containing the identity element 1. The Cayley digraph X = Cay(G, S) of G with respect to S is defined by V(X) = G, E(X) = {(g,sg...

NORMAL 6-VALENT CAYLEY GRAPHS OF ABELIAN GROUPS

Abstract : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6 was presented.