Work

Resonance Graphs that are Daisy Cubes: from Hypercubes to Independent Sets via Resonant Sets

Year: 2026

Type: article

Abstract: 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.

Source: Bulletin of the Malaysian Mathematical Sciences Society

DOI: 10.1007/s40840-026-02122-5

Authors: Simon Brezovnik, Zhongyuan Che, Niko Tratnik, Petra Žigert Pleteršek

Institutions: University of Ljubljana, Institute of Mathematics, Physics, and Mechanics, Pennsylvania State University, University of Maribor

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Javna Agencija za Raziskovalno Dejavnost RS