Mutual-visibility in strong products of graphs via total mutual-visibility

Cicerone, Serafino (author), Di Stefano, Gabriele (author), Klavžar, Sandi (author), Yero, Ismael G. (author)

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

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