English

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

Combinatorics 2021-12-21 v1

Abstract

Let Z(G){\rm Z}(G) and gp(G){\rm gp}(G) be the zero forcing number and the general position number of a graph GG, respectively. Known results imply that gp(T)Z(T)+1{\rm gp}(T)\ge {\rm Z}(T) + 1 holds for every nontrivial tree TT. It is proved that the result extends to block graphs. For connected, unicyclic graphs GG it is proved that gp(G)Z(G){\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 gp(G)Z(G){\rm gp}(G) \ge {\rm Z}(G) holds.

Keywords

Cite

@article{arxiv.2112.09999,
  title  = {Zero forcing number versus general position number in tree-like graphs},
  author = {Hongbo Hua and Xinying Hua and Sandi Klavžar},
  journal= {arXiv preprint arXiv:2112.09999},
  year   = {2021}
}
R2 v1 2026-06-24T08:23:14.086Z