Resolvability and convexity properties in the Sierpiński product of graphs

Henning, Michael A. (avtor), Klavžar, Sandi (avtor), Yero, Ismael G. (avtor)

Let $G$ and $H$ be graphs and let $f \colon V(G)\rightarrow V(H)$ be a function. The Sierpiński product of $G$ and $H$ with respect to $f$, denoted by $G \otimes _f H$, is defined as the graph on the vertex set $V(G)\times V(H)$, consisting of $|V(G)|$ copies of $H$; for every edge $gg'$ of $G$ there is an edge between copies $gH$ and $g'H$ of $H$ associated with the vertices $g$ and $g'$ of $G$, respectively, of the form $(g,f(g'))(g',f(g))$. The Sierpiński metric dimension and the upper Sierpiński metric dimension of two graphs are determined. Closed formulas are determined for Sierpiński products of trees, and for Sierpiński products of two cycles where the second factor is a triangle. We also prove that the layers with respect to the second factor in a Sierpiński product graph are convex.

• Jezik: Angleški jezik
• Ključne besede: Sierpiński product of graphs, metric dimension, trees, convex subgraph
• 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
• Leto izida: 2024
• Št. strani: 17 str.
• Številčenje: Vol. 21, iss. 1, art. 3
• PID: 20.500.12556/RUL-152589
• UDK: 519.17
• ISSN pri članku: 1660-5446
• DOI: 10.1007/s00009-023-02544-6
• COBISS.SI-ID: 172901379
• Datum objave v RUL: 29.11.2023

Gradivo je del revije

• Naslov: Mediterranean journal of mathematics
• Skrajšan naslov: Mediterr. j. math.
• Založnik: Springer Nature
• ISSN: 1660-5446
• COBISS.SI-ID: 13561433

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: Sierpinskijev produkt grafov, metrična dimenzija, drevesa, konveksni podgrafi