Paired Eternal Domination in Grid Graphs and k-Trees

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dc.contributor.authorPenner, Georgia
dc.date.accessioned2023-09-19T16:04:52Z
dc.date.available2023-09-19T16:04:52Z
dc.date.copyright2023en_US
dc.date.issued2023-09-19
dc.description.abstractWe explore the paired eternal domination number on two different classes of graphs. The paired eternal domination problem is a variation on eternal domination where guards must remain paired after every move. We first consider grid graphs, finding exact values for 2xn grids. We also find bounds on the paired eternal domination number, but not tight bounds, for larger grid graphs, in particular 3xn and 4xn grids. For a restricted subset of k-trees with small maximum degree, we extend a prior result on trees to these k-trees, allowing the use of a previously invented algorithm to determine the paired eternal domination number of these graphs.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelUndergraduateen_US
dc.description.sponsorshipValerie Kuehne Undergraduate Research Awards (VKURA)en_US
dc.identifier.urihttp://hdl.handle.net/1828/15404
dc.language.isoenen_US
dc.subjectGraph theoryen_US
dc.subjectDominating setsen_US
dc.subjectEternal dominationen_US
dc.subjectPaired dominationen_US
dc.titlePaired Eternal Domination in Grid Graphs and k-Treesen_US
dc.typePosteren_US

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