Variations on the power domination problem: Hypergraphs and robustness

dc.contributor.advisor Leslie Hogben Morrison, Beth
dc.contributor.department Mathematics 2020-06-26T19:54:57.000 2020-06-30T03:21:53Z 2020-06-30T03:21:53Z Fri May 01 00:00:00 UTC 2020 2021-06-16 2020-01-01
dc.description.abstract <p>The power domination problem seeks to find the minimum number of sensors called phasor measurement units (PMUs) to monitor an electric power network. In this dissertation, we present two variations of the power domination problem.</p> <p>The first variation is infectious power domination, which is a new way to generalize the power domination problem to hypergraphs using the infection rule from Bergen et al. (2018). We compare to the previous generalization by Chang and Roussel (2015). We examine general bounds; graph families such as complete k-partite hypergraphs, circular arc hypergraphs, and trees; and the impact of edge/vertex removal, linear sums, Cartesian products, and weak coronas.</p> <p>The second variation considers how the minimum number of sensors and their placement changes when k sensors are allowed to fail. The PMU-defect robust power domination number is also a novel parameter, generalizing the work done by Pai, Chang, and Wang (2010) by allowing multiple sensors to be placed at the same location. We give general bounds, explicit values for some complete bipartite graphs, and computational results for small square grid graphs. We also give a new proof of the power domination number for trees and conjecture the PMU-defect robust power domination number for trees.</p>
dc.format.mimetype application/pdf
dc.identifier archive/
dc.identifier.articleid 8938
dc.identifier.contextkey 18242507
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath etd/17931
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 21:31:19 UTC 2022
dc.subject.keywords domination
dc.subject.keywords hypergraphs
dc.subject.keywords infection number
dc.subject.keywords power domination
dc.title Variations on the power domination problem: Hypergraphs and robustness
dc.type article
dc.type.genre thesis
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48 Mathematics thesis Doctor of Philosophy
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