Reconfiguration graphs of zero forcing sets
Publication Date
4-15-2023
Document Type
Article
Publication Title
Discrete Applied Mathematics
Volume
329
DOI
10.1016/j.dam.2023.01.027
First Page
126
Last Page
139
Abstract
This paper begins the study of reconfiguration of zero forcing sets, and more specifically, the zero forcing graph. Given a base graph G, its zero forcing graph, Z(G), is the graph whose vertices are the minimum zero forcing sets of G with an edge between vertices B and B′ of Z(G) if and only if B can be obtained from B′ by changing a single vertex of G. It is shown that the zero forcing graph of a forest is connected, but that many zero forcing graphs are disconnected. We characterize the base graphs whose zero forcing graphs are complete graphs, and show that the star cannot be a zero forcing graph. We show that computing Z(G) takes 2Θ(n) operations in the worst case for a graph G of order n.
Keywords
Reconfiguration, Zero forcing, Zero forcing graph
Department
Mathematics and Statistics
Recommended Citation
Jesse Geneson, Ruth Haas, and Leslie Hogben. "Reconfiguration graphs of zero forcing sets" Discrete Applied Mathematics (2023): 126-139. https://doi.org/10.1016/j.dam.2023.01.027
