Resonance graphs that are daisy cubes: from hypercubes to independent sets via resonant sets

Brezovnik, Simon (avtor), Che, Zhongyuan (avtor), Tratnik, Niko (avtor), Žigert Pleteršek, Petra (avtor)

Let $G$ be a plane elementary bipartite graph whose infinite face is forcing. We first provide a bijection between the set of maximal hypercubes of its resonance graph and the set of maximal resonant sets of $G$. In the special case where $G$ is a peripherally 2-colorable graph, it follows that there is a bijection between the set of maximal hypercubes of its resonance graph and the set of maximal independent sets of a tree that is the inner dual of $G$. We then show that the resonance graph of a plane bipartite graph $G$ is a daisy cube if and only if it is the simplex graph of the complement of a forest. Finally, we characterize trees with at most five maximal independent sets to determine daisy cubes that are simplex graphs of complements of trees and have at most five maximal vertices.

• Jezik: Angleški jezik
• Ključne besede: daisy cube, resonance graph, simplex graph
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FS - Fakulteta za strojništvo ; FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: 22 str.
• Številčenje: Vol. 49, iss. 4, art. 152
• PID: 20.500.12556/RUL-186034
• UDK: 519.17
• ISSN pri članku: 0126-6705
• DOI: 10.1007/s40840-026-02122-5
• COBISS.SI-ID: 287669507
• Datum objave v RUL: 26.08.2026

Gradivo je del revije

• Naslov: Bulletin of the Malaysian Mathematical Sciences Society
• Skrajšan naslov: Bull. Malays. Math. Sci. Soc.
• Založnik: Malaysian Mathematical Society, Springer Nature
• ISSN: 0126-6705
• COBISS.SI-ID: 515781657

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: resonančni graf, simpleksni graf