Abstract
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.
