Non-regular square bipartite designs Original Research Article

A square bipartite design is a pair of square 0–1 matrices A and B satisfying the following matrix equation: image ATB=λJ+diag(d),where J is a matrix filled with all ones, λ is a positive integer, and diag(d) is a diagonal matrix with the vector d in the diagonal. We give a characterization of a class of non-regular square bipartite designs; our result generalizes some earlier results of De Bruijn and Erd image s, Lehman, and Gasparyan.