3 research outputs found
The Cyclic Groups with them-DCI Property
AbstractFor a finite groupGand a subsetSofGwhich does not contain the identity ofG,let Cay(G,S)denote the Cayley graph ofGwith respect toS.If, for all subsetsS, TofGof sizem,Cay(G,S)≅Cay(G,T)impliesSα=Tfor someα∈Aut(G), thenGis said to have them-DCI property. In this paper, a classification is presented of the cyclic groups with them-DCI property, which is reasonably complete
Generalized quaternion groups with the -DCI property
A Cayley digraph Cay(G,S) of a finite group with respect to a subset
of is said to be a CI-digraph if for every Cayley digraph Cay(G,T)
isomorphic to Cay(G,S), there exists an automorphism of such that
. A finite group is said to have the -DCI property for some
positive integer if all -valent Cayley digraphs of are CI-digraphs,
and is said to be a DCI-group if has the -DCI property for all . Let be a generalized quaternion group of order
with an integer , and let have the -DCI
property for some . It is shown in this paper that is
odd, and is not divisible by for any prime . Furthermore,
if is a power of a prime , then has the -DCI
property if and only if is odd, and either or .Comment: 1