Abstract
- A subset of initially infected vertices of a graph is called zero forcing if we can infect the entire graph by iteratively applying the following process. At each step, any infected vertex which has a unique uninfected neighbor, infects this neighbor. The zero forcing number of is the minimum cardinality of a zero forcing set in . We study the zero forcing number of various classes of graphs, including graphs of large girth, -free graphs for a fixed bipartite graph , and random and pseudorandom graphs.