发表机构
Department of Mathematics and Computer Science, Wheaton College, IL（伊利诺伊州惠顿学院数学与计算机科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究零强制参数相对于图阶的差异，给出极小零强制集基数差及传播时间差的上界，并证明对无限图族紧致。
AI 中文摘要
零强制是一种由图的顶点上的颜色变化规则描述的过程。在本文中，我们最大化各种零强制参数相对于图阶的差异。首先，我们找到了最大和最小规模的极小零强制集（不含真零强制子集的集合）的基数之差的上下界，并证明该界对无限图族是紧的。此外，我们推导了任意图的最小零强制集的最大与最小传播时间之间差异的上界，并证明该界对无限图族是紧的。
英文摘要
Zero forcing is a process described by a color change rule on the vertices of a graph. In this paper, we maximize the discrepancy between various zero forcing parameters relative to graph order. First, we find an upper bound on the difference in cardinality between minimal zero forcing sets (sets containing no proper zero forcing subset) of maximum and minimum size, and we show that this bound is sharp for an infinite family of graphs. Furthermore, we derive an upper bound for the discrepancy between the maximum and minimum propagation times of the minimum zero forcing sets of any graph, showing this bound is sharp for an infinite family of graphs.
Comments18 pages, 7 figures, 2 tables
