Zero forcing propagation time on oriented graphs
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....
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| Veröffentlicht in: | Discrete Applied Mathematics 2017-06, Vol.224, p.45-59 |
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| container_title | Discrete Applied Mathematics |
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| creator | Berliner, Adam Bozeman, Chassidy Butler, Steve Catral, Minerva Hogben, Leslie Kroschel, Brenda Lin, Jephian C.-H. Warnberg, Nathan Young, Michael |
| description | 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. |
| doi_str_mv | 10.1016/j.dam.2017.02.017 |
| format | Article |
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| ispartof | Discrete Applied Mathematics, 2017-06, Vol.224, p.45-59 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete; Free E-Journal (出版社公開部分のみ） |
| subjects | Color Coloring Graph coloring Graph theory Graphs Hessenberg path Oriented graphs Propagation Propagation time Throttling Zero forcing process |
| title | Zero forcing propagation time on oriented graphs |
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