2025/05/12 by Zhongyuan Che, Zhibo Chen, Che, Zhongyuan +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2505.07992
It has recently been shown in [Discrete Appl. Math. \bf 366 (2025) 75--85] that the resonance graph of a plane elementary bipartite graph G is a daisy cube if and only if G is peripherally 2-colorable. Let G be a peripherally 2-colorable graph and R(G) be its resonance graph. We provide a decomposition structure of R(G) with respect to an arbitrary finite face of G together with a proper labelling for the vertex set of R(G). An algorithm is obtained to generate a proper labelling for all perfect matchings of G which induces an isometric embedding of R(G) as a daisy cube into an n-dimensional hypercube, where n is the isometric dimension of R(G). Moreover, the algorithm can be applied to generate such a proper labelling for all perfect matchings of any plane weakly elementary bipartite graph whose each elementary component with more than two vertices is peripherally 2-colorable. We also compare two binary codings for all perfect matchings of G which induces distinct structures on R(G): one as a daisy cube and the other as a finite distributive, respectively.