On the power domination number of the Cartesian product of graphs

On the power domination number of the Cartesian product of graphs

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We give a brief survey about the existing results on the power domination of the Cartesian product of graphs, and improve two of the results by determining the exact power domination numbers of two families of graphs, namely, the cylinder Pn□Cmand the tori Cn□Cm. We also establish the power dominati...

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Main Authors: K.M. Koh, K.W. Soh
Format: Article
Language:English
Published: Taylor & Francis Group 2019-12-01
Series:AKCE International Journal of Graphs and Combinatorics
Online Access:http://www.sciencedirect.com/science/article/pii/S0972860016301633
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spelling doaj-eae212353a774e478056da02754be3172020-11-25T03:21:40ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002019-12-01163253257On the power domination number of the Cartesian product of graphsK.M. Koh0K.W. Soh1Engineering Systems and Design, Singapore University of Technology and Design, Singapore; Corresponding author.Department of Engineering Science, The University of Auckland, New ZealandWe give a brief survey about the existing results on the power domination of the Cartesian product of graphs, and improve two of the results by determining the exact power domination numbers of two families of graphs, namely, the cylinder Pn□Cmand the tori Cn□Cm. We also establish the power domination number for Kn□K1,m, the Cartesian product of a complete graph and a star. Keywords: Electric power monitoring, Power domination, Zero forcing, Cartesian producthttp://www.sciencedirect.com/science/article/pii/S0972860016301633
collection DOAJ
language English
format Article
sources DOAJ
author K.M. Koh
K.W. Soh
spellingShingle K.M. Koh
K.W. Soh
On the power domination number of the Cartesian product of graphs
AKCE International Journal of Graphs and Combinatorics
author_facet K.M. Koh
K.W. Soh
author_sort K.M. Koh
title On the power domination number of the Cartesian product of graphs
title_short On the power domination number of the Cartesian product of graphs
title_full On the power domination number of the Cartesian product of graphs
title_fullStr On the power domination number of the Cartesian product of graphs
title_full_unstemmed On the power domination number of the Cartesian product of graphs
title_sort on the power domination number of the cartesian product of graphs
publisher Taylor & Francis Group
series AKCE International Journal of Graphs and Combinatorics
issn 0972-8600
publishDate 2019-12-01
description We give a brief survey about the existing results on the power domination of the Cartesian product of graphs, and improve two of the results by determining the exact power domination numbers of two families of graphs, namely, the cylinder Pn□Cmand the tori Cn□Cm. We also establish the power domination number for Kn□K1,m, the Cartesian product of a complete graph and a star. Keywords: Electric power monitoring, Power domination, Zero forcing, Cartesian product
url http://www.sciencedirect.com/science/article/pii/S0972860016301633
work_keys_str_mv AT kmkoh onthepowerdominationnumberofthecartesianproductofgraphs
AT kwsoh onthepowerdominationnumberofthecartesianproductofgraphs
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