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- W3185729178 abstract "A family of decompositions $mathcal{G} = left{ {{mathcal{G}_0},{mathcal{G}_1}, ldots ldots ,{mathcal{G}_{{text{r}} - {text{l}}}}} right.} $ of a complete bipartite graph K <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</inf> , n is a set of r mutually orthogonal graph squares (MOGS) if ${mathcal{G}_i}$ and ${mathcal{G}_j}$ are orthogonal for all i j, ∈{0, 1, … −, r 1}, and i ≠ j. For any subgraph G of K <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</inf> n, with n edges, N (n G, ) denotes the maximum number r in a largest possible set $mathcal{G} = left{ {{mathcal{G}_0},{mathcal{G}_1}, ldots ldots ,{mathcal{G}_{{text{r}} - {text{l}}}}} right.} $ of MOGS of K <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</inf> , n by G . In this paper, we compute two extensions N (n, G) = r ≥ 4, for n = 11, we have G = (4K <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1,2</inf> ∪3K <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</inf> ), and n = 13, G will be (3K <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1,2</inf> ∪7K <inf xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</inf> )." @default.
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- W3185729178 date "2021-07-03" @default.
- W3185729178 modified "2023-10-17" @default.
- W3185729178 title "On Construction Mutually Orthogonal Disjoint Unions of Small Certain Trees Graph Squares" @default.
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- W3185729178 doi "https://doi.org/10.1109/iceem52022.2021.9480661" @default.
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