Zero forcing for sign patterns

We introduce a new variant of zero forcing—signed zero forcing. The classical zero forcing number provides an upper bound on the maximum nullity of a matrix with a given graph (i.e. zero-nonzero pattern). Our new variant provides an analogous bound for the maximum nullity of a matrix with a given sign pattern. This allows us to compute, for instance, the maximum nullity of a Z  -matrix whose graph is L(Kn)L(Kn), the line graph of a clique.