On Fragile Power Domination
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908456856846336 |
|---|---|
| author | Bjorkman, Beth English, Sean Koch, Johnathan Verga, Amanda |
| author_facet | Bjorkman, Beth English, Sean Koch, Johnathan Verga, Amanda |
| contents | Power domination is a graph theoretic model which captures how phasor measurement units (PMUs) can be used to monitor a power grid. Fragile power domination takes into account the fact that PMUs may break or otherwise fail. In this model, each sensor fails independently with probability $q\in [0,1]$ and the surviving sensors monitor the grid according to classical power domination.
We study the expected number of observed nodes under the fragile power domination model. We give a characterization for when two networks and initial sensor placements will behave the same according to this expectation. We also show how to control the behavior of this expectation by adding structure to a network. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14620 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Fragile Power Domination Bjorkman, Beth English, Sean Koch, Johnathan Verga, Amanda Combinatorics 05C69, 68R10, 05C57, 62H22 Power domination is a graph theoretic model which captures how phasor measurement units (PMUs) can be used to monitor a power grid. Fragile power domination takes into account the fact that PMUs may break or otherwise fail. In this model, each sensor fails independently with probability $q\in [0,1]$ and the surviving sensors monitor the grid according to classical power domination. We study the expected number of observed nodes under the fragile power domination model. We give a characterization for when two networks and initial sensor placements will behave the same according to this expectation. We also show how to control the behavior of this expectation by adding structure to a network. |
| title | On Fragile Power Domination |
| topic | Combinatorics 05C69, 68R10, 05C57, 62H22 |
| url | https://arxiv.org/abs/2507.14620 |