2024/05/29 by Brezovnik, Simon, Che, Zhongyuan, Tratnik, Niko +1
#05C70 05C10 05C75 05C92 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2405.18862
Let G be a plane elementary bipartite graph whose infinite face is forcing. We show that there is a bijection between the set of maximal resonant sets of G and the set of maximal hypercubes of its resonance graph R(G). Moreover, if G is a peripherally 2-colorable graph whose inner dual is G^*, we then establish a bijection between the set of maximal hypercubes of its resonance graph R(G) and the set of maximal independent sets of G^*. Next, we present a characterization on when the resonance graph of a plane elementary bipartite graph G is a daisy cube in terms of the daisy cube constructed from the set of all independent sets of G^*. The obtained result is also extended to plane weakly elementary bipartite graphs. Finally, two algorithms which provide a proper labelling for the vertex set of R(G) as a daisy cube are presented.