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On Mutually Orthogonal Disjoint Copies of Graph Squares


Abstract


A family of decompositions \{\mathcal{G}_{0},\mathcal{G}_{1},...,% \mathcal{G}_{k-1}\} of a complete bipartite graph K_{n,n} is a set of k \textit{mutually orthogonal graph squares} (MOGS) if \mathcal{G}_{i} and \mathcal{G}_{j} \ are orthogonal for all i,j\in \{0,1,...,k-1\} and % i\neq j. For any subgraph G of K_{n,n} with n edges, N(n,G) denotes the maximum number k in a largest possible set(Error rendering LaTeX formula) of (MOGS) of K_{n,n} by G. Our objective of this paper is to compute N(n,G)=k\geq 3 where G represents disjoint copies of certain subgraphs of K_{n,n}.

DOI Code: 10.1285/i15900932v36n2p89

Keywords: Orthogonal graph squares; Orthogonal double cover; Mutually orthogonal Latin squares

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