笛卡尔积图的f-点稳定数

The f-Vertex Stability Number of Cartesian Product Graphs

摘要: 图的不变量点稳定数是最近的热点问题之一，它被应用于设计算法解决图论的某些特定问题。设$f$ 是图不变量，图$G$ 的$f$ -点稳定数$v{s}_f\left(G\right)$ 定义为使得$f\left(G-V^{\prime }\right)\ne f\left(G\right)$ 成立的最小点子集$V^{\prime }$ 的基数。在本文中，通过不变量$f$ 的性质，讨论笛卡尔积图的$f$ -点稳定数的界。

Abstract: The invariant vertex stability number of graph is one of the recent hot topics, which is applied to design algorithms to solve certain problems in graph theory. Let $f$ be an invariant of graphs, and the $f$ -vertex stability number $v{s}_f\left(G\right)$ of a graph $G$ is defined as the cardinality of the minimum vertex subset $V^{\prime }$ such that $f\left(G-V^{\prime }\right)\ne f\left(G\right)$ . In this paper, we discuss the bounds of the $f$ -vertex stability number for Cartesian product graphs through the properties of the invariant $f$ .