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On Construction Mutually Orthogonal Disjoint Unions of Small Certain Trees Graph Squares.
Oral Presentation , Page 121-125 (5)
Volume Title: 2nd IEEE International Conference on Electronic Eng., Faculty of Electronic Eng., Menouf, Egypt, 3-4 July. 2021
Authors
Abstract
A family of decompositions {G₀,G₁,...,G_{r-1}} of a complete bipartite graph K_{n,n} is a set of r mutually orthogonal graph squares (MOGS) if G_{i} and G_{j} are orthogonal for all i,j∈{0,1,...,r-1} and i≠j. For any subgraph G of K_{n,n} with n edges, N(n,G) denotes the maximum number r in a largest possible set {G₀,G₁,...,G_{r-1}} of MOGS of K_{n,n} by G. In this paper we compute two extensions of the well-known N(n,G)=r≥4, where n=11, G=(4K_{1,2}∪3K₂), and n=13, G=(3K_{1,2}∪7K₂).
A family of decompositions {G₀,G₁,...,G_{r-1}} of a complete bipartite graph K_{n,n} is a set of r mutually orthogonal graph squares (MOGS) if G_{i} and G_{j} are orthogonal for all i,j∈{0,1,...,r-1} and i≠j. For any subgraph G of K_{n,n} with n edges, N(n,G) denotes the maximum number r in a largest possible set {G₀,G₁,...,G_{r-1}} of MOGS of K_{n,n} by G. In this paper we compute two extensions of the well-known N(n,G)=r≥4, where n=11, G=(4K_{1,2}∪3K₂), and n=13, G=(3K_{1,2}∪7K₂).
A family of decompositions {G₀,G₁,...,G_{r-1}} of a complete bipartite graph K_{n,n} is a set of r mutually orthogonal graph squares (MOGS) if G_{i} and G_{j} are orthogonal for all i,j∈{0,1,...,r-1} and i≠j. For any subgraph G of K_{n,n} with n edges, N(n,G) denotes the maximum number r in a largest possible set {G₀,G₁,...,G_{r-1}} of MOGS of K_{n,n} by G. In this paper we compute two extensions of the well-known N(n,G)=r≥4, where n=11, G=(4K_{1,2}∪3K₂), and n=13, G=(3K_{1,2}∪7K₂).
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