标题： 网格状和环状图中的支配序列 显示英文标题

标题： Dominating sequences in grid-like and toroidal graphs

摘要： 一个最长序列$S$的不同顶点的图$G$，使得每个顶点$S$支配某个顶点，该顶点不被其前驱顶点支配，称为Grundy支配序列；$S$的长度是$G$的Grundy支配数。 在本文中，我们研究了四个标准图积中的Grundy支配数：笛卡尔积、字典积、直接积和强积。 对于每种积，我们给出了Grundy支配数的下界，结果发现对于字典积是精确的，对于强积则是一个猜想。 在大多数情况下，确定了路径和/或环的积的精确Grundy支配数。 显示英文摘要

摘要： A longest sequence $S$ of distinct vertices of a graph $G$ such that each vertex of $S$ dominates some vertex that is not dominated by its preceding vertices, is called a Grundy dominating sequence; the length of $S$ is the Grundy domination number of $G$. In this paper we study the Grundy domination number in the four standard graph products: the Cartesian, the lexicographic, the direct, and the strong product. For each of the products we present a lower bound for the Grundy domination number which turns out to be exact for the lexicographic product and is conjectured to be exact for the strong product. In most of the cases exact Grundy domination numbers are determined for products of paths and/or cycles.