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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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MD5: 1FF2D4123EC505ED6452BFCE80E0F483
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https://www.sciencedirect.com/science/article/pii/S0166218X24002907
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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
UDC:
519.17
ISSN on article:
0166-218X
DOI:
10.1016/j.dam.2024.06.038
COBISS.SI-ID:
201822467
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
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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