Another conjecture of TxGraffiti concerning zero forcing and domination in graphs

Abstract

This paper proves a conjecture generated by the artificial intelligence conjecturing program called \emph{TxGraffiti}. More specifically, we show that if $G$ is a connected, cubic, and claw-free graph, then $Z(G)\le \gamma (G)+2$, where $Z(G)$ and $\gamma (G)$ denote the zero forcing number and the domination number of $G$, respectively. Furthermore, we provide a complete characterization of graphs that achieve this bound. Notably, this bound improves the known upper bounds for the zero forcing number of connected, cubic, and claw-free graphs.

Cited by in corpus (1)

• Automated conjecturing with \emph{TxGraffiti}