Zero Forcing in triangulations

Abstract

In this work, we study the zero forcing problem and some of its variants regarding the connectivity of the subgraph generated by the zero forcing set. A set Z of vertices from a graph G is said to be a zero forcing set of G if iteratively adding to it unique neighboring vertices of those vertices V ( G ) ∖ Z already in Z results in the entire vertex set V ( G ) of G . The zero forcing number Z ( G ) of G is the minimum cardinality of a zero forcing set of G . In this paper, we establish tight combinatorial bounds for zero forcing, total zero forcing and connected zero forcing for maximal outerplanar graphs. We also present a lower bound for zero forcing for near-triangulations.