两个图乘积的最大失败迫零集
Maximal failed zero forcing sets for products of two graphs
摘要：
设$G$是一个简单的有限图，其顶点集为$V(G)$，边集为$E(G)$，其中每个顶点都是蓝色或白色的.使用以下颜色变化规则定义$G$上的标准迫零过程：令$S$为$G$的所有初始蓝色顶点的集合，并令$u \in S$。如果$v$是$G$中与$u$相邻的唯一白色顶点，则将$v$染成蓝色，并通过将$v$添加到$S$来更新$S$。如果$S = V(G)$经过有限次的颜色变化规则的迭代，我们说$S$是$G$的迫零集。否则，我们说$S$是一个失败的迫零集。在本文中，我们构造了图积（例如笛卡儿积、强积、字典积和冠）的最大失败迫零集。特别地，我们考虑两条路，两个圈，和两个完全图的产品。
英文摘要：
Let $G$ be a simple, finite graph with vertex set $V(G)$ and edge set $E(G)$, where each vertex is either colored blue or white. Define the standard zero forcing process on $G$ with the following color-change rule: let $S$ be the set of all initially blue vertices of $G$ and let $u \in S$. If $v$ is the unique white vertex adjacent to $u$ in $G$, color $v$ blue and update $S$ by adding $v$ to $S$. If $S = V(G)$ after a finite number of iterations of the color-change rule, we say that $S$ is a zero forcing set for $G$. Otherwise, we say that $S$ is a failed zero forcing set. In this paper, we construct maximal failed zero forcing sets for graph products such as Cartesian products, strong products, lexicographic products, and coronas. In particular, we consider products of two paths, two cycles, and two complete graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
