方格棋盘上的支配子和总支配子着色

K. Sowndarya, Y. Naidu
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引用次数: 0

摘要

如果图G的每一个顶点都支配某一颜色类的每一个顶点,则称图G的固有着色为支配着色。满足主色条件所需的最小色类数称为主色数,用χd(G)表示。总的支配着色被定义为G的固有着色,其性质是G的每个顶点都支配至少一个颜色类(除了类本身)的所有顶点。满足总支配子着色条件所需的最小色类数称为总支配子色数,用χtd(G)表示。本文讨论了方格棋盘上主、车的支配子和总支配子着色参数,并给出了这些棋盘图的支配子色数和总支配子色数的取值。
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Dominator and Total Dominator Coloring on Square Chessboard
The proper coloring of a graph G is said to be a dominator coloring if each vertex of the graph dominates every vertex of some color class. The minimum number of color classes required to satisfy the condition of dominator coloring is said to be dominator chromatic number which is denoted by χd(G). Total dominator coloring is defined to be a proper coloring of G with a property that every vertex of G dominates all the vertices of at least one color class (other than the class itself). The minimum number of color classes required to satisfy the condition of total dominator coloring is called total dominator chromatic number and is denoted by χtd(G). In this paper, we would discuss the dominator and total dominator coloring parameters of bishops and rooks on square chessboard and give the values for dominator chromatic number and total dominator chromatic number for these chessboard graphs.
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