Another conjecture of TxGraffiti concerning zero forcing and domination in graphs
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
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| _version_ | 1866909394656034816 |
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| author | Davila, Randy R. |
| author_facet | Davila, Randy R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Another conjecture of TxGraffiti concerning zero forcing and domination in graphs Davila, Randy R. Combinatorics 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. |
| title | Another conjecture of TxGraffiti concerning zero forcing and domination in graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.19231 |