Resonance graphs and a binary coding of perfect matchings of outerplane bipartite graphsBrezovnik, Simon (Avtor) Tratnik, Niko (Avtor) Žigert Pleteršek, Petra (Avtor) graph theoryresonance graphsbipartite graphsThe 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. 20232024-03-20 07:52:39Znanstveno delo87532sl