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

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

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.

• Language: English
• Keywords: daisy cube, resonance graph, simplex graph
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 22 str.
• Numbering: Vol. 49, iss. 4, art. 152
• PID: 20.500.12556/RUL-186034
• UDC: 519.17
• ISSN on article: 0126-6705
• DOI: 10.1007/s40840-026-02122-5
• COBISS.SI-ID: 287669507
• Publication date in RUL: 26.08.2026

Record is a part of a journal

• Title: Bulletin of the Malaysian Mathematical Sciences Society
• Shortened title: Bull. Malays. Math. Sci. Soc.
• Publisher: Malaysian Mathematical Society, Springer Nature
• ISSN: 0126-6705
• COBISS.SI-ID: 515781657

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: resonančni graf, simpleksni graf