Resonance graphs of plane bipartite graphs as daisy cubes

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

We characterize plane bipartite graphs whose resonance graphs are daisy cubes, and therefore generalize related results on resonance graphs of benzenoid graphs, catacondensed even ring systems, as well as 2-connected outerplane bipartite graphs. Firstly, we prove that if $G$ is a plane elementary bipartite graph other than $K_2$, then the resonance graph of $G$ is a daisy cube if and only if the Fries number of $G$ equals the number of finite faces of $G$. Next, we extend the above characterization from plane elementary bipartite graphs to plane bipartite graphs and show that the resonance graph of a plane bipartite graph $G$ is a daisy cube if and only if $G$ is weakly elementary bipartite such that each of its elementary component $G_i$ other than $K_2$ holds the property that the Fries number of $G_i$ equals the number of finite faces of $G_i$ . Along the way, we provide a structural characterization for a plane elementary bipartite graph whose resonance graph is a daisy cube, and show that a Cartesian product graph is a daisy cube if and only if all of its nontrivial factors are daisy cubes.

• Language: English
• Keywords: daisy cube, Fries number, peripherally 2-colorable graph, plane elementary bipartite graph, weakly elementary bipartite graph, plane weakly elementary bipartite graph, resonance graph
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 75-85
• Numbering: Vol. 366
• PID: 20.500.12556/RUL-167006
• UDC: 519.17
• ISSN on article: 0166-218X
• DOI: 10.1016/j.dam.2025.01.017
• COBISS.SI-ID: 224635651
• Publication date in RUL: 03.02.2025

Record is a part of a journal

• Title: Discrete applied mathematics
• Shortened title: Discrete appl. math.
• Publisher: Elsevier
• ISSN: 0166-218X
• COBISS.SI-ID: 25342464

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: ravni elementarni bipartitni graf, šibko elementarni bipartitni graf, ravni šibko elementarni bipartitni graf, resonančni graf, marjetična kocka, teorija grafov