Zero forcing in iterated line digraphs

Journal article

Ferrero, Daniela, Kalinowski, Thomas and Stephen, Sudeep. (2019). Zero forcing in iterated line digraphs. Discrete Applied Mathematics. 255, pp. 198-208. https://doi.org/10.1016/j.dam.2018.08.019
AuthorsFerrero, Daniela, Kalinowski, Thomas and Stephen, Sudeep
Abstract

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.

Keywordsminimum rank; zero forcing; power domination; iterated line digraphs
Year2019
JournalDiscrete Applied Mathematics
Journal citation255, pp. 198-208
PublisherElsevier B.V.
ISSN0166-218X
Digital Object Identifier (DOI)https://doi.org/10.1016/j.dam.2018.08.019
Scopus EID2-s2.0-85054797696
Page range198-208
Publisher's version
License
All rights reserved
File Access Level
Controlled
Output statusPublished
Publication dates
Online17 Oct 2018
Publication process dates
Accepted24 Aug 2018
Deposited30 Nov 2023
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