On Mutually Orthogonal Disjoint Copies of Graph Squares
Abstract
A family of decompositions
of a complete bipartite graph
is a set of
\textit{mutually orthogonal graph squares}
if
and
\ are orthogonal for all
and
. For any subgraph
of
with
edges,
denotes the maximum number
in a largest possible set(Error rendering LaTeX formula) of
of
by
. Our objective of this paper is to compute
where
represents disjoint copies of certain subgraphs of
.
![\{\mathcal{G}_{0},\mathcal{G}_{1},...,% \mathcal{G}_{k-1}\}](https://853417.krfdn.asia/plugins/generic/latexRender/cache/34fcf91d06a07e218144fe4c92fb8c84.png)
![K_{n,n}](https://853417.krfdn.asia/plugins/generic/latexRender/cache/cea543bdfb1e9855d6054e8a98e0b685.png)
![k](https://853417.krfdn.asia/plugins/generic/latexRender/cache/8ce4b16b22b58894aa86c421e8759df3.png)
![(MOGS)](https://853417.krfdn.asia/plugins/generic/latexRender/cache/72b74729bc562a53b5c05de87cf70773.png)
![\mathcal{G}_{i}](https://853417.krfdn.asia/plugins/generic/latexRender/cache/85dc1d5e0eea0957b421a9bdadc84958.png)
![\mathcal{G}_{j}](https://853417.krfdn.asia/plugins/generic/latexRender/cache/2520407a17b71e6b65500123216cd9e2.png)
![i,j\in \{0,1,...,k-1\}](https://853417.krfdn.asia/plugins/generic/latexRender/cache/13e3435ea75a0b375db5ff03aa07109f.png)
![% i\neq j](https://853417.krfdn.asia/plugins/generic/latexRender/cache/f41631cccb615c19226dda82d4467f7f.png)
![G](https://853417.krfdn.asia/plugins/generic/latexRender/cache/dfcf28d0734569a6a693bc8194de62bf.png)
![K_{n,n}](https://853417.krfdn.asia/plugins/generic/latexRender/cache/cea543bdfb1e9855d6054e8a98e0b685.png)
![n](https://853417.krfdn.asia/plugins/generic/latexRender/cache/7b8b965ad4bca0e41ab51de7b31363a1.png)
![N(n,G)](https://853417.krfdn.asia/plugins/generic/latexRender/cache/234cda59fdfbfdf35d31a0d004fe93db.png)
![k](https://853417.krfdn.asia/plugins/generic/latexRender/cache/8ce4b16b22b58894aa86c421e8759df3.png)
![(MOGS)](https://853417.krfdn.asia/plugins/generic/latexRender/cache/72b74729bc562a53b5c05de87cf70773.png)
![K_{n,n}](https://853417.krfdn.asia/plugins/generic/latexRender/cache/cea543bdfb1e9855d6054e8a98e0b685.png)
![G](https://853417.krfdn.asia/plugins/generic/latexRender/cache/dfcf28d0734569a6a693bc8194de62bf.png)
![N(n,G)=k\geq 3](https://853417.krfdn.asia/plugins/generic/latexRender/cache/fa12082027a9adbd61decd05e0dcae88.png)
![G](https://853417.krfdn.asia/plugins/generic/latexRender/cache/dfcf28d0734569a6a693bc8194de62bf.png)
![K_{n,n}](https://853417.krfdn.asia/plugins/generic/latexRender/cache/cea543bdfb1e9855d6054e8a98e0b685.png)
DOI Code:
10.1285/i15900932v36n2p89
Keywords:
Orthogonal graph squares; Orthogonal double cover; Mutually orthogonal Latin squares
Full Text: PDF