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Mutual-visibility in strong products of graphs via total mutual-visibility
ID Cicerone, Serafino (Author), ID Di Stefano, Gabriele (Author), ID Klavžar, Sandi (Author), ID Yero, Ismael G. (Author)

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Abstract
Let $G$ be a graph and $X\subseteq V(G)$. Then $X$ is a mutual-visibility set if each pair of vertices from $X$ is connected by a geodesic with no internal vertex in $X$. The mutual-visibility number $\mu(G)$ of $G$ is the cardinality of a largest mutual-visibility set. In this paper, the mutual-visibility number of strong product graphs is investigated. As a tool for this, total mutual-visibility sets are introduced. Along the way, basic properties of such sets are presented. The (total) mutual-visibility number of strong products is bounded from below in two ways, and determined exactly for strong grids of arbitrary dimension. Strong prisms are studied separately and a couple of tight bounds for their mutual-visibility number are given.

Language:English
Keywords:mutual-visibility set, mutual-visibility number, total mutual-visibility set, strong product of graphs
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publication status:Published
Publication version:Version of Record
Publication date:01.12.2024
Year:2024
Number of pages:Str. 136-146
Numbering:Vol. 358
PID:20.500.12556/RUL-163141 This link opens in a new window
UDC:519.17
ISSN on article:0166-218X
DOI:10.1016/j.dam.2024.06.038 This link opens in a new window
COBISS.SI-ID:201822467 This link opens in a new window
Publication date in RUL:02.10.2024
Views:126
Downloads:21
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Record is a part of a journal

Title:Discrete applied mathematics
Shortened title:Discrete appl. math.
Publisher:Elsevier
ISSN:0166-218X
COBISS.SI-ID:25342464 This link opens in a new window

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, število vzajemne vidnosti, množica celotne vzajemne vidnosti, krepki produkt grafov

Projects

Funder:Other - Other funder or multiple funders
Funding programme:European Union - NextGenerationEU
Project number:ECS00000041 - VITALITY - CUP J97G22000170005
Name:Italian Ministry of University and Research (MUR) National Innovation Ecosystem

Funder:Other - Other funder or multiple funders
Funding programme:Italian National Group for Scientific Computation
Acronym:GNCS-INdAM

Funder:ARRS - Slovenian Research Agency
Project number:P1-0297
Name:Teorija grafov

Funder:ARRS - Slovenian Research Agency
Project number:N1-0218
Name:Prepletanje geometrije, topologije in algebre v strukturni in topološki teoriji grafov

Funder:ARRS - Slovenian Research Agency
Project number:N1-0285
Name:Metrični problemi v grafih in hipergrafih

Funder:Other - Other funder or multiple funders
Funding programme:Spanish Ministry of Science and Innovation
Project number:PID2019-105824GB-I00

Funder:Other - Other funder or multiple funders
Funding programme:Ministerio de Educación, Cultura y Deporte, Spain
Project number:CAS21/00100
Name:“José Castillejo” program for young researchers

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