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Title:Mutual-visibility problems on graphs of diameter two
Authors:ID Cicerone, Serafino (Author)
ID Di Stefano, Gabriele (Author)
ID Klavžar, Sandi (Author)
ID Yero, Ismael G. (Author)
Files:.pdf PDF - Presentation file, download (558,13 KB)
MD5: 0D24608BA2A2073D9130C1681F9E08A9
 
URL URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0195669824000805
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:The mutual-visibility problem in a graph $G$ asks for the cardinality of a largest set of vertices $S\subseteq V(G)$ so that for any two vertices $x,y \in S$ there is a shortest $x,y$-path $P$ so that all internal vertices of $P$ are not in $S$. This is also said as $x,y$ are visible with respect to $S$, or $S$-visible for short. Variations of this problem are known, based on the extension of the visibility property of vertices that are in and/or outside $S$. Such variations are called total, outer and dual mutual-visibility problems. This work is focused on studying the corresponding four visibility parameters in graphs of diameter two, throughout showing bounds and/or closed formulae for these parameters. The mutual-visibility problem in the Cartesian product of two complete graphs is equivalent to (an instance of) the celebrated Zarankiewicz's problem. Here we study the dual and outer mutual-visibility problem for the Cartesian product of two complete graphs and all the mutual-visibility problems for the direct product of such graphs as well. We also study all the mutual-visibility problems for the line graphs of complete and complete bipartite graphs. As a consequence of this study, we present several relationships between the mentioned problems and some instances of the classical Turán problem. Moreover, we study the visibility problems for cographs and several non-trivial diameter-two graphs of minimum size.
Keywords:mutual-visibility set, mutual-visibility number, diameter-two graphs, line graphs, cographs
Publication status:Published
Publication version:Version of Record
Publication date:01.08.2024
Year of publishing:2024
Number of pages:16 str.
Numbering:Vol. 120, [article no.] 103995
PID:20.500.12556/DiRROS-19008 New window
UDC:519.17
ISSN on article:0195-6698
DOI:10.1016/j.ejc.2024.103995 New window
COBISS.SI-ID:196753923 New window
Note:
Publication date in DiRROS:27.05.2024
Views:126
Downloads:112
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Record is a part of a journal

Title:European journal of combinatorics
Shortened title:Eur. j. comb.
Publisher:Elsevier
ISSN:0195-6698
COBISS.SI-ID:25427968 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:N1-0218
Name:Prepletanje geometrije, topologije in algebre v strukturni in topološki teoriji grafov

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

Funder:Other - Other funder or multiple funders
Funding programme:Geospatial based Environment for Optimisation Systems Addressing Fire Emergencies
Project number:H2020-691161
Acronym:GEO-SAFE

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

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:Ayudas para la recualificación del sistema universitario español para 2021–2023, en el marco del Real Decreto 289/2021, de 20 de abril de 2021

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, grafi premera dva, grafi povezav, kografi


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