Zero Forcing

Speaker: Dieter Rautenbach, Ulm University

Date: 05 apr 2017, 16h.

Place: Room 407, Bloco H, IME, Campus Gragoatá, UFF.

Abstract: A set $Z$ of vertices of a graph $G$ is a zero forcing set of $G$ if initially labeling all vertices in $Z$ with $1$ and all remaining vertices of $G$ with $0$, and then, iteratively and as long as possible, changing the label of some vertex $u$ from $0$ to $1$ if $u$ is the only neighbor with label $0$ of some vertex with label $1$, results in the entire vertex set of $G$. The zero forcing number $Z(G)$, defined as the minimum order of a zero forcing set of $G$, was proposed as an upper bound of the corank of matrices associated with $G$, and was also considered in connection with quantum physics and logic circuits. In view of the computational hardness of the zero forcing number, upper and lower bounds are of interest. We discuss such bounds and some of the corresponding extremal graphs.

Note: Joint work with M. Gentner, L. D. Penso, and U. S. Souza.