Classes of Symmetric Cayley Graphs over Finite Abelian Groups of Degrees 4 and 6

The present work is devoted to characterize the family of symmetric undirected Cayley graphs over finite Abelian groups for degrees 4 and 6.Comment: 12 pages. A previous version of some of the results in this paper where first announced at 2010 International Workshop on Optimal Interconnection Networks (IWONT 2010). It is accessible at http://upcommons.upc.edu/revistes/handle/2099/1037

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