Leaky Positive Semidefinite Forcing on Graphs

Fuente: arXiv
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Autori principali: Elias, Olivia, Farish, Ian, King, Emrys, Kyei, Josh, Moruzzi Jr, Ryan
Natura: Preprint
Pubblicazione: 2023
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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