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arXiv · 2312.10154

Leaky Positive Semidefinite Forcing on Graphs

Olivia Elias·Ian Farish·Emrys King·Josh Kyei·Ryan Moruzzi Jr
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Abstract

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.

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Olivia Elias, Ian Farish, Emrys King, Josh Kyei, Ryan Moruzzi Jr. 2024-03-03. Leaky Positive Semidefinite Forcing on Graphs. https://doi.org/10.2140/involve.2025.18.719

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