Zero forcing number: Results for computation and comparison with other graph parameters
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The zero forcing number of a graph is the minimum size of a zero forcing set. This parameter is useful in the minimum rank/maximum nullity problem, as it gives an upper bound to the maximum nullity. Results for determining graphs with extreme zero forcing numbers, for determining the zero forcing number of a graph with a cut-vertex, and for determining the zero forcing number of unicyclic graphs are presented. The zero forcing number is compared to the path cover number and the maximum nullity with equality of zero forcing number and path cover number shown for all cacti and equality of zero forcing number and maximum nullity shown for a subset of cacti.