On The Embedding Of Groups And Designs In A Difference Block Design

A difference BIBD is a balanced incomplete block design on a group, which is constructed by transferring a regular perfect difference system by a subgroup of its point set. There is an obvious bijection between these BIBDs and some copies of their point sets as two sets. In this paper, we investigate the algebraic structure of these block designs by defining a group-isomorphism between them and their point sets. It has been done by defining some relations between the independent-graphs of difference BIBDs and some Cayley graphs of their point sets. It has been shown that some Cayley graphs are embedded in the independent-graph of difference BIBDs as a spanning subgraphs. In order to find these relations, we find out a configuration ordering on these BIBDs, also we have also obtained some results about the classification of these BIBDs. This paper deals with difference BIBDs with even numbers of points.