Variety of mutual-visibility problems in graphs

Cicerone, Serafino (avtor), Di Stefano, Gabriele (avtor), Drožđek, Lara (avtor), Hedžet, Jaka (avtor), Klavžar, Sandi (avtor), Yero, Ismael G. (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: mutual-visibility, total mutual-visibility, dual mutual-visibility number, outer mutual-visibility, grid graphs, torus graphs, computational complexity
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.09.2023
• Leto izida: 2023
• Št. strani: 13 str.
• Številčenje: Vol. 974, art. no. ǂ114096
• PID: 20.500.12556/RUL-155652
• UDK: 519.17
• ISSN pri članku: 0304-3975
• DOI: 10.1016/j.tcs.2023.114096
• COBISS.SI-ID: 161787907
• Datum objave v RUL: 10.04.2024

Gradivo je del revije

• Naslov: Theoretical computer science
• Skrajšan naslov: Theor. comp. sci.
• Založnik: Elsevier
• ISSN: 0304-3975
• COBISS.SI-ID: 26525952

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: vzajemna vidnost, celotna vzajemna vidnost, število dualne vzajemne vidnosti, število zunanje vzajemne vidnosti, rešetke, torusni grafi, računska zahtevnost