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.
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