Resonance Graphs and a Binary Coding of Perfect Matchings of Outerplane Bipartite Graphs

The aim of this paper is to investigate resonance graphs of 2- connected outerplane bipartite graphs, which include various families of molecular graphs. Firstly, we present an algorithm for a binary coding of perfect matchings of these graphs. Further, 2- connected outerplane bipartite graphs with isomorphic resonance graphs are considered. In particular, it is shown that if two 2- connected outerplane bipartite graphs are evenly homeomorphic, then its resonance graphs are isomorphic. Moreover, we prove that for any 2-connected outerplane bipartite graph G there exists a catacondensed even ring systems H such that the resonance graphs of G and H are isomorphic. We conclude with the characterization of 2-connected outerplane bipartite graphs whose resonance graphs are daisy cubes.