This M.Sc. thesis is based on the following paper: Istvan Kovacs, Aleksander Malnic, Dragan Marusic, Stefko Miklavic., One-matcching bi-Cayley graphs over abelian groups, European Journal of Combinatorics 30(2009) 602-616. Let e a group and e a subset of such that , where is the identity element of . The Cayley digraph over with respect to is a graph with vertex set and edge set . If , then is an undirected graph and it is called a Cayley graph. Let e subsets of a group uch that and
