On Mutually Orthogonal Disjoint Copies of Graph Squares

A family of decompositions {G0,G1, ...,Gk−1} of a complete bipartite graph Kn,n is a set of k mutually orthogonal graph squares (M OGS) if Gi and Gj are orthogonal for all i, j∈ {0,1, ..., k−1} and i6=j. For any subgraph G of Kn,n with n edges, N(n, G) denotes the maximum number k in a largest possible set {G0,G1, ...,Gk−1}of (M OGS) of Kn,n by G.Our objective of this paper is to compute N(n, G) =k≥3 where G represents disjoint copies of certain subgraphs of Kn,n.