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Failed power
domination in grids, cylinders, and tori
Isabel T. Byrne, Gretchen L. Matthews, Nikita M. Patel, Anuradha G. Trivedi and Margaret A. Winslow |
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Vol. 16 (2023), No. 4, 705–717
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Abstract |
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The power domination number of a graph is the minimum number of vertices required to monitor the graph. Here, the notion of monitoring is given by a set of rules for power system monitoring where vertices model phasor management units (PMU) in a power network. We consider the failed power domination number of a graph , , a recently introduced graph parameter. Any set of vertices of whose cardinality is greater than will dominate the graph. The failed power domination number also allows one to consider PMU (or node) failure. Indeed, any set of vertices will monitor the network even in the presence of node failures. We establish the failed power domination number for products of paths and cycles including square grids, tori, and hypercubes and provide bounds for the failed power domination number of square cylinders. |
Keywords
failed power domination, graph product, grid, power
domination
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Mathematical Subject Classification
Primary: 05C15, 05C78
Secondary: 05C50
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Milestones
Received: 20 July 2022
Revised: 19 October 2022
Accepted: 27 October 2022
Published: 31 October 2023
Communicated by Glenn Hurlbert
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Authors |
| Isabel T. Byrne | |
| Department of Mathematical
Sciences University of Delaware Newark, DE United States |
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| Gretchen L. Matthews | |
| Department of Mathematics Virginia Tech Blacksburg, VA United States |
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| Nikita M. Patel | |
| Department of Computer Science Virginia Tech Blacksburg, VA United States |
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| Anuradha G. Trivedi | |
| Department of Biomedical
Engineering Georgia Tech and Emory University Atlanta, GA United States |
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| Margaret A. Winslow | |
| Department of Mathematics Virginia Tech Blacksburg, VA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
