Resonance Graphs that are Daisy Cubes: from Hypercubes to Independent Sets via Resonant Sets
Abstract
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.
Fields of Study & Subjects
Advanced Graph Theory Research
Publication details
- Journal / source
- Bulletin of the Malaysian Mathematical Sciences Society
- Publisher
- Springer Science and Business Media LLC
- Volume
- 49
- Issue
- 4
- Publication date
- 28 July 2026
- Language
- EN
- Document type
- Book chapter