A perfect 2-coloring of a graph \(\varGamma\) with matrix \(M=\{m_{ij}\}_{i, j=1, 2}\) is a coloring of the vertices \(\varGamma\) with colors called \(\{1, 2\}\) such that the number of vertices of color j adjacent to a fixed vertex of color i is equal to \(m_{ij}\). We state the matrix M is the parameter matrix. Each class of an equitable partition is the vertices with the same color. In this article, we classify the parameter matrices of whole perfect 2-colorings of the Johnson graph J(9, 4).

中文翻译：

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Johnson图J的完美2色（9，4）

的曲线图的一个完美2着色\（\ varGamma \）与矩阵\（M = \ {M_ {IJ} \} _ {I，J = 1，2} \）是顶点的着色\（\ varGamma \）具有称为\（\ {1，2 \} \）的颜色，使得与颜色i的固定顶点相邻的颜色j的顶点数等于\（m_ {ij} \）。我们说矩阵M是参数矩阵。相等分区的每一类都是具有相同颜色的顶点。在本文中，我们对Johnson图J（9，4）的整体完全2色的参数矩阵进行分类。