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arXiv · 2406.19231

Another conjecture of TxGraffiti concerning zero forcing and domination in graphs

Randy R. Davila
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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 $Z(G) \le γ(G) + 2$, where $Z(G)$ and $γ(G)$ 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.

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Randy R. Davila. 2024-11-18. Another conjecture of TxGraffiti concerning zero forcing and domination in graphs. https://arxiv.org/abs/2406.19231

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