Zero Forcing Propagation Time on Oriented Graphs

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2017-06-19
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Berliner, Adam
Bozeman, Chassidy
Butler, Steve
Catral, Minerva
Hogben, Leslie
Kroschel, Brenda
Lin, Jephian
Warnberg, Nathan
Young, Michael
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Electrical and Computer EngineeringMathematics
Abstract

Zero forcing is an iterative coloring procedure on a graph that starts by initially coloring vertices white and blue and then repeatedly applies the following rule: if any blue vertex has a unique (out-)neighbor that is colored white, then that neighbor is forced to change color from white to blue. An initial set of blue vertices that can force the entire graph to blue is called a zero forcing set. In this paper we consider the minimum number of iterations needed for this color change rule to color all of the vertices blue, also known as the propagation time, for oriented graphs. We produce oriented graphs with both high and low propagation times, consider the possible propagation times for the orientations of a fixed graph, and look at balancing the size of a zero forcing set and the propagation time.

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This is a manuscript of an article published as Berliner, Adam, Chassidy Bozeman, Steve Butler, Minerva Catral, Leslie Hogben, Brenda Kroschel, Jephian C-H Lin, Nathan Warnberg, and Michael Young. "Zero forcing propagation time on oriented graphs." Discrete Applied Mathematics 224 (2017): 45-59. DOI: 10.1016/j.dam.2017.02.017. Posted with permission.

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Sun Jan 01 00:00:00 UTC 2017
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