Campus Units
Mathematics
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
2-15-2019
Journal or Book Title
Discrete Applied Mathematics
Volume
254
First Page
33
Last Page
46
DOI
10.1016/j.dam.2018.06.017
Abstract
Zero forcing is a process on a graph that colors vertices blue by starting with some of the vertices blue and applying a color change rule. Throttling minimizes the sum of the size of the initial blue vertex set and the number of the time steps needed to color the graph. We study throttling for positive semidefinite zero forcing. We establish a tight lower bound on the positive semidefinite throttling number as a function of the order, maximum degree, and positive semidefinite zero forcing number of the graph, and determine the positive semidefinite throttling numbers of paths, cycles, and full binary trees. We characterize the graphs that have extreme positive semidefinite throttling numbers.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Copyright Owner
Elsevier B.V.
Copyright Date
2018
Language
en
File Format
application/pdf
Recommended Citation
Carlson, Joshua; Hogben, Leslie; Kritschgau, Jürgen; Lorenzen, Kate; Ross, Michael S.; Selken, Seth; and Valle Martinez, Vicente, "Throttling positive semidefinite zero forcing propagation time on graphs" (2019). Mathematics Publications. 206.
https://lib.dr.iastate.edu/math_pubs/206
Comments
This is a manuscript of an article published as Carlson, Joshua, Leslie Hogben, Jürgen Kritschgau, Kate Lorenzen, Michael S. Ross, Seth Selken, and Vicente Valle Martinez. "Throttling positive semidefinite zero forcing propagation time on graphs." Discrete Applied Mathematics 254 (2019): 33-46. DOI: 10.1016/j.dam.2018.06.017. Posted with permission.