Leaky Positive Semidefinite Forcing on Graphs
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866912506030587904 |
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| author | Elias, Olivia Farish, Ian King, Emrys Kyei, Josh Moruzzi Jr, Ryan |
| author_facet | Elias, Olivia Farish, Ian King, Emrys Kyei, Josh Moruzzi Jr, Ryan |
| contents | We introduce $\ell$-leaky positive semidefinite forcing and the $\ell$-leaky positive semidefinite number of a graph, $Z_{(\ell)}^+{G}$, which combines the positive semidefinite color change rule with the addition of leaks to the graph. Furthermore, we determine general properties of $Z_{(\ell)}^+{G}$ and $Z_{(\ell)}^+{G}$ for various graphs, including path graphs, complete graphs, wheel graphs, complete bipartite graphs, trees, hypercubes, and prisms. We also define $\ell$-leaky positive semidefinite forts with the purpose of unveiling differences between $\ell$-leaky standard forcing and $\ell$-leaky positive semidefinite forcing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10154 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Leaky Positive Semidefinite Forcing on Graphs Elias, Olivia Farish, Ian King, Emrys Kyei, Josh Moruzzi Jr, Ryan Combinatorics 05C50, 05C76 We introduce $\ell$-leaky positive semidefinite forcing and the $\ell$-leaky positive semidefinite number of a graph, $Z_{(\ell)}^+{G}$, which combines the positive semidefinite color change rule with the addition of leaks to the graph. Furthermore, we determine general properties of $Z_{(\ell)}^+{G}$ and $Z_{(\ell)}^+{G}$ for various graphs, including path graphs, complete graphs, wheel graphs, complete bipartite graphs, trees, hypercubes, and prisms. We also define $\ell$-leaky positive semidefinite forts with the purpose of unveiling differences between $\ell$-leaky standard forcing and $\ell$-leaky positive semidefinite forcing. |
| title | Leaky Positive Semidefinite Forcing on Graphs |
| topic | Combinatorics 05C50, 05C76 |
| url | https://arxiv.org/abs/2312.10154 |