Speaker
Dr
István Kovács
(University of Primorska)
Description
For a finite group G and a subset S of G such that 1 is not in S the Cayley graph Cay(G,S) has vertex set G and arcs in the form (x,sx) where x runs over G and s runs over S. A Cayley graph Cay(G,S) is called a CI-graph if for every subset T with Cay(G,T) being isomorphic to Cay(G,S), T=f(S) for some automorphism f of G. The group G is called a DCI-group if every Cayley graph of G is a CI-graph, and it is called a CI-group if every undirected Cayley graph of G is a CI-graph (note that, Cay(G,S) is undirected when the set S is closed under taking inverse elements). Although there is a restrictive list of potentional CI-groups (Li-Lu-Pálfy, 2007), only a few classes of groups have been proved to be indeed CI; in several cases the proof was obtained by studying the Schur rings over the given group. In my talk I review the Schur ring method and also present some recent results based on a joint work with Yan-Quan Feng (Beijing Jiaotong University, China).
Primary author
Dr
István Kovács
(University of Primorska)
