Mutual-Visibility Sets in Cartesian Products of Paths and Cycles

For a given graph G , the mutual-visibility problem asks for the largest set of vertices M ⊆ V ( G ) with the property that for any pair of vertices u , v ∈ M there exists a shortest u , v -path of G that does not pass through any other vertex in M . The mutual-visibility problem for Cartesian prod...

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Published in:	Resultate der Mathematik Vol. 79; no. 3; p. 116
Main Authors:	Korže, Danilo, Vesel, Aleksander
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.05.2024 Springer Nature B.V
Subjects:	Apexes Cartesian coordinates Codes Distributed processing Graph theory Graphs Mathematics Mathematics and Statistics Visibility Mutual-visibility set mutual-visibility number 05C12 68R10 Cartesian product 05C38
ISSN:	1422-6383, 1420-9012
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Abstract	For a given graph G , the mutual-visibility problem asks for the largest set of vertices M ⊆ V ( G ) with the property that for any pair of vertices u , v ∈ M there exists a shortest u , v -path of G that does not pass through any other vertex in M . The mutual-visibility problem for Cartesian products of a cycle and a path, as well as for Cartesian products of two cycles, is considered. Optimal solutions are provided for the majority of Cartesian products of a cycle and a path, while for the other family of graphs, the problem is completely solved.
AbstractList	For a given graph G, the mutual-visibility problem asks for the largest set of vertices M⊆V(G) with the property that for any pair of vertices u,v∈M there exists a shortest u, v-path of G that does not pass through any other vertex in M. The mutual-visibility problem for Cartesian products of a cycle and a path, as well as for Cartesian products of two cycles, is considered. Optimal solutions are provided for the majority of Cartesian products of a cycle and a path, while for the other family of graphs, the problem is completely solved. For a given graph G , the mutual-visibility problem asks for the largest set of vertices $$M \subseteq V(G)$$ M ⊆ V ( G ) with the property that for any pair of vertices $$u,v \in M$$ u , v ∈ M there exists a shortest u , v -path of G that does not pass through any other vertex in M . The mutual-visibility problem for Cartesian products of a cycle and a path, as well as for Cartesian products of two cycles, is considered. Optimal solutions are provided for the majority of Cartesian products of a cycle and a path, while for the other family of graphs, the problem is completely solved. For a given graph G , the mutual-visibility problem asks for the largest set of vertices M ⊆ V ( G ) with the property that for any pair of vertices u , v ∈ M there exists a shortest u , v -path of G that does not pass through any other vertex in M . The mutual-visibility problem for Cartesian products of a cycle and a path, as well as for Cartesian products of two cycles, is considered. Optimal solutions are provided for the majority of Cartesian products of a cycle and a path, while for the other family of graphs, the problem is completely solved.
ArticleNumber	116
Author	Vesel, Aleksander Korže, Danilo
Author_xml	– sequence: 1 givenname: Danilo surname: Korže fullname: Korže, Danilo organization: Faculty of Electrical Engineering and Computer Science, University of Maribor – sequence: 2 givenname: Aleksander orcidid: 0000-0003-3705-0071 surname: Vesel fullname: Vesel, Aleksander email: aleksander.vesel@um.si organization: Faculty of Natural Sciences and Mathematics, University of Maribor
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Cites_doi	10.1016/j.procs.2023.08.219 10.1016/j.tcs.2023.114096 10.1016/j.ic.2016.09.005 10.1007/978-3-030-39881-1_4 10.1016/j.tcs.2020.10.033 10.7151/dmgt.2496 10.1016/j.amc.2022.127619 10.1145/3571306.3571401 10.1007/s00025-021-01438-x
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Snippet	For a given graph G , the mutual-visibility problem asks for the largest set of vertices M ⊆ V ( G ) with the property that for any pair of vertices u , v ∈ M... For a given graph G , the mutual-visibility problem asks for the largest set of vertices $$M \subseteq V(G)$$ M ⊆ V ( G ) with the property that for any pair... For a given graph G, the mutual-visibility problem asks for the largest set of vertices M⊆V(G) with the property that for any pair of vertices u,v∈M there...
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StartPage	116
SubjectTerms	Apexes Cartesian coordinates Codes Distributed processing Graph theory Graphs Mathematics Mathematics and Statistics Visibility
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Title	Mutual-Visibility Sets in Cartesian Products of Paths and Cycles
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