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A Novel Construction of Mutually Orthogonal Three Disjoint Union of Certain Trees Squares |
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PP: 7-11 |
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doi:10.18576/amis/170102
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Author(s) |
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R. El-Shanawany,
S. Nada,
A. Elrokh,
E. Sallam,
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Abstract |
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| A family of decompositions {G0,G1,...,Gk−1} of a complete bipartite graph Kn,n is a set of k mutually orthogonal graph squares(MOGS)ifGi andGj areorthogonalforalli,j∈{0,1,...,k−1}andi̸= j.ForanysubgraphGofKn,n withnedges,N(n,G) denotes the maximum number k in a largest possible set {G0,G1,...,Gk−1} of MOGS of Kn,n by G. In this paper we compute some new extensions of the well-known N(n,G) ≥ 3, using a novel approach, where G represents disjoint unions of certain small trees subgraphs of Kn,n.
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