Resonance graphs of plane bipartite graphs as daisy cubes

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

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.

• Jezik: Angleški jezik
• Ključne besede: daisy cube, Fries number, peripherally 2-colorable graph, plane elementary bipartite graph, weakly elementary bipartite graph, plane weakly elementary bipartite graph, resonance graph
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FS - Fakulteta za strojništvo
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2025
• Št. strani: Str. 75-85
• Številčenje: Vol. 366
• PID: 20.500.12556/RUL-167006
• UDK: 519.17
• ISSN pri članku: 0166-218X
• DOI: 10.1016/j.dam.2025.01.017
• COBISS.SI-ID: 224635651
• Datum objave v RUL: 03.02.2025

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