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

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.