Isometric embeddings of resonance graphs as finite distributive lattices

Abstract Let G be a plane bipartite graph admitting a perfect matching, and let R ( G ) denote its resonance graph. It is known that any connected resonance graph can be isometrically embedded into hypercubes as a finite distributive lattice. Let $$n_0(G)$$ n 0 ( G ) denote the number of finite faces of G without forbidden edges on their peripheries. We show that any connected R ( G ) has isometric dimension at least $$n_0(G)$$ n 0 ( G ) , and the lower bound is attained if and only if G is a plane weakly elementary bipartite graph such that the infinite face of each nontrivial elementary component of G is forcing. We also design an algorithm to produce a binary coding on the vertex set of R ( G ) which induces an isometric embedding of R ( G ) as a finite distributive lattice into a hypercube of dimension $$n_0(G)$$ n 0 ( G ) .