论文标题
在无限多径图的完美着色上
On perfect colorings of infinite multipath graphs
论文作者
论文摘要
如果每个半径的颜色结构在图中仅取决于球中心的颜色，则给定图的顶点的着色称为完美。让$ n $成为一个积极的整数。我们考虑无限路径图的词典产物和图$ g $，可以是$ n $ Vertices上的完整图形或空图。我们完整地描述了完美的着色，并具有此类图形产品的任意颜色。
A coloring of vertices of a given graph is called perfect if the color structure of each ball of radius $1$ in the graph depends only on the color of the ball center. Let $n$ be a positive integer. We consider a lexicographic product of the infinite path graph and a graph $G$ that can be either the complete or empty graph on $n$ vertices. We give a complete description of perfect colorings with an arbitrary number of colors of such graph products.
