论文标题
跳跃规则
The Hopping Forcing Rule
论文作者
论文摘要
零强迫是在图表上播放的组合游戏，可用于使用颜色更改规则的重复应用来对信息的传播进行建模。通常，零强制参数是最终用给定颜色更改规则染色每个顶点蓝色所需的初始蓝色顶点的最小数量。此外，节流数量最小化了初始蓝色顶点的数量和所有顶点变成蓝色所花费的时间。 2013年，Barioli等人。为了证明各种零强迫参数的次要单调地板本身是零强迫参数，添加了一个名为“跳跃”的新规则，称为“跳”，以证明各种零强迫参数的次要单调地板。在本文中，我们独立于其他经典规则来检查跳颜色变化规则。具体来说，我们研究了跳跃数量和跳跃数量。我们研究了这些数字与各种图理论参数（例如顶点连接和独立数）以及其他零强迫参数相关的方式。
Zero forcing is a combinatorial game played on graphs that can be used to model the spread of information with repeated applications of a color change rule. In general, a zero forcing parameter is the minimum number of initial blue vertices that are needed to eventually color every vertex blue with a given color change rule. Furthermore, the throttling number minimizes the sum of the number of initial blue vertices and the time taken for all vertices to become blue. In 2013, Barioli et al. added a new rule, called hopping, to existing color change rules in order to demonstrate that the minor monotone floor of various zero forcing parameters is itself, a zero forcing parameter. In this paper, we examine the hopping color change rule independently from the other classic rules. Specifically, we study the hopping forcing number and the hopping throttling number. We investigate the ways in which these numbers are related to various graph theory parameters (such as vertex connectivity and independence number) as well as other zero forcing parameters.
