Q.Sergio Hiroki Koike – On isomorphism of cyclic Haar graphs

Abstract: Given a cyclic group and a subset of this group, we define a cyclic Haar graphs as a bipartite graph with two copies of the cyclic group and a edge {i,i+j} with i in one partition and i+j in the other.
Given a fix cyclic Haar graph H(n,A). We say that A is an HI-set if for any subset B of the cyclic group such that the cyclic Haar graphs H(n,A) and H(n,B) are isomorphic then there is an element f in the affine group of the cyclic group which maps B into A. The graph isomorphism problem in the class of cyclic Haar graphs is, esentially, to describe the pairs A and B for which the graphs H(n,A) and H(n,B) are isomorphic but there is not such function which maps B into A.
In this talk we will discuss some tools to find which graphs are isomorphic and there is an element f in the affine group of the cyclic group which maps B into A.