论文标题
加权零强迫的传播时间
Propagation time for weighted zero forcing
论文作者
论文摘要
零强迫是一个图形着色过程，该过程被定义为界限最小等级和图形最大无效的工具。它也已用于研究量子系统的控制和监视电力网络。 2017 AIM研讨会“零强迫及其应用”中的问题之一是探索边缘加权的概率零强迫，如果在标准零强迫着色规则下进行强迫，则边缘的权重决定了成功力的概率。 在本文中，我们调查了完成加权零强迫着色过程（称为预期传播时间）的预期时间，以及以至少$α$（称为$α$ convidence Expagitation time的概率）完成该过程的时间。我们演示了如何使用Markov矩阵找到任何边缘加权图的预期和置信度传播时间。我们还确定了各种边缘加权图的家族的预期和置信度传播时间，包括完整的图，恒星，路径和周期。
Zero forcing is a graph coloring process that was defined as a tool for bounding the minimum rank and maximum nullity of a graph. It has also been used for studying control of quantum systems and monitoring electrical power networks. One of the problems from the 2017 AIM workshop "Zero forcing and its applications" was to explore edge-weighted probabilistic zero forcing, where edges have weights that determine the probability of a successful force if forcing is possible under the standard zero forcing coloring rule. In this paper, we investigate the expected time to complete the weighted zero forcing coloring process, known as the expected propagation time, as well as the time for the process to be completed with probability at least $α$, known as the $α$-confidence propagation time. We demonstrate how to find the expected and confidence propagation times of any edge-weighted graph using Markov matrices. We also determine the expected and confidence propagation times for various families of edge-weighted graphs including complete graphs, stars, paths, and cycles.
