Zero forcing number versus general position number in tree-like graphs

• Published in: arXiv.org
• Main Authors: Hua, Hongbo, Hua, Xinying, Klavžar, Sandi
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.12.2021
• Subjects: Graphs
• ISSN: 2331-8422

Let \({\rm Z}(G)\) and \({\rm gp}(G)\) be the zero forcing number and the general position number of a graph \(G\), respectively. Known results imply that \({\rm gp}(T)\ge {\rm Z}(T) + 1\) holds for every nontrivial tree \(T\). It is proved that the result extends to block graphs. For connected, unicyclic graphs \(G\) it is proved that \({\rm gp}(G) \ge {\rm Z}(G)\). The result extends neither to bicyclic graphs nor to quasi-trees. Nevertheless, a large class of quasi-trees is found for which \({\rm gp}(G) \ge {\rm Z}(G)\) holds.