标题： 支配集的笛卡尔乘积的表征 显示英文标题

标题： A characterization of well-dominated Cartesian products

摘要： 如果一个图的所有最小支配集的基数相同，那么这个图是良好支配的。 在本文中，我们证明了每个连通的良好支配笛卡尔乘积至少有一个因子是完全图，这使我们能够对两个因子的阶数都至少为$2$的连通的良好支配笛卡尔乘积进行完整的表征。 特别是，我们证明了$G\,\Box\,H$是良好支配的当且仅当$G\,\Box\,H = P_3 \,\Box\,K_3$或$G\,\Box\,H= K_n \,\Box\,K_n$对某个$n\ge 2$成立。 显示英文摘要

摘要： A graph is well-dominated if all its minimal dominating sets have the same cardinality. In this paper we prove that at least one factor of every connected, well-dominated Cartesian product is a complete graph, which then allows us to give a complete characterization of the connected, well-dominated Cartesian products if both factors have order at least $2$. In particular, we show that $G\,\Box\,H$ is well-dominated if and only if $G\,\Box\,H = P_3 \,\Box\,K_3$ or $G\,\Box\,H= K_n \,\Box\,K_n$ for some $n\ge 2$.