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Preprint . 2020
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Product Throttling for Power Domination.

Product throttling for power domination
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2021Embargo end date: 01 Jan 2020 United States Publisher:US DOEJournal:Proposed for presentation at the Joint Mathematics Meeting held January 6-9, 2021.Funded by:NSF | Career Advancement for Wo...
Authors: Anderson, Sarah; Collins, Karen; Ferrero, Daniela; Hogben, Leslie; Mayer, Carolyn; Trenk, Ann; Walker, Shanise;

doi: 10.2172/1839518 , 10.48550/arxiv.2010.16315

arXiv: 2010.16315

handle: 20.500.12876/4vGXA9Zr

Product Throttling for Power Domination.

Abstract

The product power throttling number of a graph is defined to study product throttling for power domination. The domination number of a graph is an upper bound for its product power throttling number. It is established that the two parameters are equal for certain families including paths, cycles, complete graphs, unit interval graphs, and grid graphs (on the plane, cylinder, and torus). Families of graphs for which the product power throttling number is less than the domination number are also exhibited. Graphs with extremely high or low product power throttling number are characterized and bounds on the product power throttling number are established.

Corrected typographical error in Remark 4.2

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Keywords

throttling, power domination, power propagation, Power domination, Graph operations (line graphs, products, etc.), product power throttling, 510, 620, 05C15, 05C57, 05C69, graph searching, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), Cartesian product, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), product throttling

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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Green