Zero Forcing on 2-connected Outerplanar Graphs

TL;DR

This paper establishes bounds on the zero forcing number for 2-connected outerplanar graphs, extending previous results for maximal outerplanar graphs by relating it to the structure of their weak duals.

Contribution

It generalizes existing bounds from maximal outerplanar graphs to all 2-connected outerplanar graphs using the weak dual structure.

Findings

Upper bound on zero forcing number is at most half the number of vertices.

Bounds are expressed in terms of the weak dual structure.

Results extend previous work on maximal outerplanar graphs.

Abstract

We determine upper and lower bounds on the zero forcing number of 2-connected outerplanar graphs in terms of the structure of the weak dual. We show that the upper bound is always at most half the number of vertices of the graph. This work generalizes work of Hern\'andez, Ranilla and Ranilla-Cortina who proved a similar result for maximal outerplanar graphs.