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Variety of mutual-visibility problems in graphs
ID Cicerone, Serafino (Author), ID Di Stefano, Gabriele (Author), ID Drožđek, Lara (Author), ID Hedžet, Jaka (Author), ID Klavžar, Sandi (Author), ID Yero, Ismael G. (Author)

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Abstract
If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u,v\}$. If each two vertices from $X$ are $X$-visible, then $X$ is a mutual-visibility set. The mutual-visibility number of $G$ is the cardinality of a largest mutual-visibility set of $G$ and has been already investigated. In this paper a variety of mutual-visibility problems is introduced based on which natural pairs of vertices are required to be $X$-visible. This yields the total, the dual, and the outer mutual-visibility numbers. We first show that these graph invariants are related to each other and to the classical mutual-visibility number, and then we prove that the three newly introduced mutual-visibility problems are computationally difficult. According to this result, we compute or bound their values for several graphs classes that include for instance grid graphs and tori. We conclude the study by presenting some inter-comparison between the values of such parameters, which is based on the computations we made for some specific families.

Language:English
Keywords:mutual-visibility, total mutual-visibility, dual mutual-visibility number, outer mutual-visibility, grid graphs, torus graphs, computational complexity
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:01.09.2023
Year:2023
Number of pages:13 str.
Numbering:Vol. 974, art. no. ǂ114096
PID:20.500.12556/RUL-155652 This link opens in a new window
UDC:519.17
ISSN on article:0304-3975
DOI:10.1016/j.tcs.2023.114096 This link opens in a new window
COBISS.SI-ID:161787907 This link opens in a new window
Publication date in RUL:10.04.2024
Views:398
Downloads:68
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Record is a part of a journal

Title:Theoretical computer science
Shortened title:Theor. comp. sci.
Publisher:Elsevier
ISSN:0304-3975
COBISS.SI-ID:26525952 This link opens in a new window

Licences

License:CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

Language:Slovenian
Keywords:vzajemna vidnost, celotna vzajemna vidnost, število dualne vzajemne vidnosti, število zunanje vzajemne vidnosti, rešetke, torusni grafi, računska zahtevnost

Projects

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

Funder:ARRS - Slovenian Research Agency
Project number:J1-2452
Name:Strukturni, optimizacijski in algoritmični problemi v geometrijskih in topoloških predstavitvah 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:European H2020 project
Project number:H2020-691161
Name:Geospatial based Environment for Optimisation Systems Addressing Fire Emergencies
Acronym:GEO-SAFE

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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