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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Vydáno v:Resultate der Mathematik Ročník 79; číslo 3; s. 116
Hlavní autoři: Korže, Danilo, Vesel, Aleksander
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.05.2024
Springer Nature B.V
Témata:
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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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-024-02139-x