Reconfiguration graphs of zero forcing sets
Discrete Applied Mathematics
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.
Reconfiguration, Zero forcing, Zero forcing graph
Mathematics and Statistics
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