A Characterization of Claw-Free Graphs using Zero Forcing Invariants
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909432025186304 |
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| author | Davila, Randy Schuerger, Houston Small, Ben |
| author_facet | Davila, Randy Schuerger, Houston Small, Ben |
| contents | We prove that the \emph{standard zero forcing number} $Z(G)$ and the \emph{positive semidefinite zero forcing number} $Z_+(G)$ are equal for all claw-free graphs $G$. This result resolves a conjecture proposed by the computer program \emph{TxGraffiti} and highlights a connection between these graph invariants in claw-free structures. As a corollary, we show that a graph $G$ is claw-free if and only if every induced subgraph $H \subseteq G$ satisfies $Z(H) = Z_+(H)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Characterization of Claw-Free Graphs using Zero Forcing Invariants Davila, Randy Schuerger, Houston Small, Ben Combinatorics We prove that the \emph{standard zero forcing number} $Z(G)$ and the \emph{positive semidefinite zero forcing number} $Z_+(G)$ are equal for all claw-free graphs $G$. This result resolves a conjecture proposed by the computer program \emph{TxGraffiti} and highlights a connection between these graph invariants in claw-free structures. As a corollary, we show that a graph $G$ is claw-free if and only if every induced subgraph $H \subseteq G$ satisfies $Z(H) = Z_+(H)$. |
| title | A Characterization of Claw-Free Graphs using Zero Forcing Invariants |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.03463 |