In this paper, partially balanced incomplete block designs with three associate classes have been constructed by using magnificent matrices, otherwise called -matrices introduced by Mohan [10]. In fact, we have tried to propose the new structures of -matrices that generate new PBIB designs along with new -graphs and also the new structures of -matrices are modifications of the structures proposed by Mohan [10]. The proposition of the new structure of -matrices has also been modified according to the requirements of the new constructions of designs along with association schemes of the new designs.

M_n-matrices, partially balanced incomplete block (PBIB) design and regular bipartite graph, M_n-graphs.