Zero forcing in iterated line digraphs
Zero forcing in iterated line digraphs
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DOI：
10.1016/j.dam.2018.08.019
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发表时间：
2017-08
期刊：
影响因子：
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通讯作者：
Daniela Ferrero;T. Kalinowski;Sudeep Stephen
中科院分区：
文献类型：
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作者：
Daniela Ferrero;T. Kalinowski;Sudeep Stephen
迫零是在线性代数中定义的图或有向图上的传播过程，以提供最小秩问题的界。有向图是物理学、计算机科学和网络科学中经常使用的模型。迫零也与功率控制有关，功率控制是一种模拟电力网络监控的传播过程，本文研究了迭代线有向图中的迫零，并给出了有向图中迫零与功率控制之间的关系。特别是，对于正则迭代线有向图，我们确定了最小秩/最大零度，迫零数和幂控制数，并提供了实现它们的结构。我们的结论是，定期迭代线有向图目前最佳的最小秩/最大零值，迫零数和功率控制数，并应用我们的结果，以确定这些参数的一些家庭的有向图经常使用的应用。
Zero forcing is a propagation process on a graph, or digraph, defined in linear algebra to provide a bound for the minimum rank problem. Independently, zero forcing was introduced in physics, computer science and network science, areas where line digraphs are frequently used as models. Zero forcing is also related to power domination, a propagation process that models the monitoring of electrical power networks.In this paper we study zero forcing in iterated line digraphs and provide a relationship between zero forcing and power domination in line digraphs. In particular, for regular iterated line digraphs we determine the minimum rank/maximum nullity, zero forcing number and power domination number, and provide constructions to attain them. We conclude that regular iterated line digraphs present optimal minimum rank/maximum nullity, zero forcing number and power domination number, and apply our results to determine those parameters on some families of digraphs often used in applications.