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<p>Let <i>G</i> 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 <i>G</i>. In the special case where <i>G</i> 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 <i>G</i>. We then show that the resonance graph of a plane bipartite graph <i>G</i> 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月28日

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  • Simon Brezovnik,
  • Zhongyuan Che,
  • Niko Tratnik,
  • Petra Žigert Pleteršek

摘要

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.