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. The path cover number of a graph is the
minimum size of a path cover. Results for comparing the parameters are
presented, with equality of zero forcing number and path cover number shown
for all cacti and equality of zero forcing number and maximum nullity for
a subset of cacti. (A cactus is a graph where each edge is in at most one
cycle.)
Keywords
zero forcing number, path cover number, maximum nullity,
cut-edge, cut-vertex, cactus
