Title

Zero forcing propagation time on oriented graphs

Department/School

Mathematics

Date

1-1-2017

Document Type

Article

Keywords

zero forcing process, propagation time, oriented graphs, Hessenberg path, throttling

DOI

https://doi.org/10.1016/j.dam.2017.02.017

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.

Published in

Discrete Applied Mathematics

Citation/Other Information

Berliner, A., Bozeman, C., Butler, S., Catral, M., Hogben, L., Kroschel, B., Lin, J. C.-H., Warnberg, N., & Young, M. (2017). Zero forcing propagation time on oriented graphs. Discrete Applied Mathematics, 224, 45–59. https://doi.org/10.1016/j.dam.2017.02.017

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