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http://dx.doi.org/10.5666/KMJ.2019.59.1.175

Bounding the Search Number of Graph Products  

Clarke, Nancy Ellen (Department of Mathematics and Statistics, Acadia University)
Messinger, Margaret-Ellen (Department of Mathematics and Computer Science, Mount Allison University)
Power, Grace (Department of Mathematics and Computer Science, Mount Allison University)
Publication Information
Kyungpook Mathematical Journal / v.59, no.1, 2019 , pp. 175-190 More about this Journal
Abstract
In this paper, we provide results for the search number of the Cartesian product of graphs. We consider graphs on opposing ends of the spectrum: paths and cliques. Our main result determines the pathwidth of the product of cliques and provides a lower bound for the search number of the product of cliques. A consequence of this result is a bound for the search number of the product of arbitrary graphs G and H based on their respective clique numbers.
Keywords
graph searching; sweeping; pathwidth;
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