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

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

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.

• Jezik: Angleški jezik
• Ključne besede: mutual-visibility set, mutual-visibility number, total mutual-visibility set, strong product of graphs
• 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: 01.12.2024
• Leto izida: 2024
• Št. strani: Str. 136-146
• Številčenje: Vol. 358
• PID: 20.500.12556/RUL-163141
• UDK: 519.17
• ISSN pri članku: 0166-218X
• DOI: 10.1016/j.dam.2024.06.038
• COBISS.SI-ID: 201822467
• Datum objave v RUL: 02.10.2024

Gradivo je del revije

• Naslov: Discrete applied mathematics
• Skrajšan naslov: Discrete appl. math.
• Založnik: Elsevier
• ISSN: 0166-218X
• COBISS.SI-ID: 25342464

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: množica vzajemne vidnosti, število vzajemne vidnosti, množica celotne vzajemne vidnosti, krepki produkt grafov