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Title:Total mutual-visibility in Hamming graphs
Authors:ID Bujtás, Csilla (Author)
ID Klavžar, Sandi (Author)
ID Tian, Jing (Author)
Files:.pdf PDF - Presentation file, download (512,21 KB)
MD5: 76C8DA0C8283EF377B0D2CDA5E2781EF
 
URL URL - Source URL, visit https://www.opuscula.agh.edu.pl/om-vol45iss1art5
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:If G is a graph and X⊆V(G), then X is a total mutual-visibility set if every pair of vertices x and y of G admits a shortest x,y-path P with V(P)∩X⊆{x,y}. The cardinality of a largest total mutual-visibility set of G is the total mutual-visibility number μt(G) of G. In this paper the total mutual-visibility number is studied on Hamming graphs, that is, Cartesian products of complete graphs. Different equivalent formulations for the problem are derived. The values μt(Kn1◻Kn2◻Kn3) are determined. It is proved that μt(Kn1◻⋯◻Knr)=O(Nr−2)▫, where N=n1+⋯+nr, and that μt(K◻,rs)=Θ(sr−2) for every r≥3, where K◻,rs denotes the Cartesian product of r copies of Ks. The main theorems are also reformulated as Turán-type results on hypergraphs.
Keywords:mutual-visibility set, total mutual-visibility set, Hamming graphs, Turán-type problem
Publication status:Published
Publication version:Version of Record
Publication date:01.01.2025
Year of publishing:2025
Number of pages:str. 63-78
Numbering:Vol. 45, no. 1
PID:20.500.12556/DiRROS-21117 New window
UDC:519.17
ISSN on article:1232-9274
DOI:10.7494/OpMath.2025.45.1.63 New window
COBISS.SI-ID:220652803 New window
Note:
Publication date in DiRROS:30.12.2024
Views:200
Downloads:90
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BUJTÁS, Csilla, KLAVŽAR, Sandi and TIAN, Jing, 2025, Total mutual-visibility in Hamming graphs. Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica : Opuscula Mathematica [online]. 2025. Vol. 45, no. 1, p. 63–78. [Accessed 7 April 2025]. DOI 10.7494/OpMath.2025.45.1.63. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=21117
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Record is a part of a journal

Title:Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica : Opuscula Mathematica
Shortened title:Rocz. Akad. Gór.-Hut. im. Stanisława Staszica, Opusc. Math.
Publisher:AGH University of Science and Technology Press
ISSN:1232-9274
COBISS.SI-ID:16179545 New window

Document is financed by a project

Funder:ARIS - Slovenian Research and Innovation Agency
Project number:P1-0297
Name:Teorija grafov
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0285
Name:Metrični problemi v grafih in hipergrafih
Funder:ARIS - Slovenian Research and Innovation Agency
Project number:N1-0355
Name:Prirejanja, transverzale in hipergrafi

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

Language:Slovenian
Keywords:množica vzajemne vidnosti, množica celotne vzajemne vidnosti, Hammingovi grafi, problem Turánovega tipa


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