The zero forcing number of the complement of a graph

Emelie Curl, Shaun Fallat, Ryan Moruzzi Jr, Carolyn Reinhart, Derek Young

Published 2022-06-08Version 1

Motivated in part by an observation that the zero forcing number for the complement of a tree on $n$ vertices is either $n-3$ or $n-1$ in one exceptional case, we consider the zero forcing number for the complement of more general graphs under some conditions, particularly those that do not contain complete bipartite induced subgraphs. We also move well beyond trees and completely study the possible zero forcing numbers for the complements of unicyclic graphs, and examine the zero forcing number for the complements of some specific families of graphs containing more than one cycle.