Resonance graphs of plane bipartite graphs as daisy cubes

We characterize all plane bipartite graphs whose resonance graphs are daisy cubes and therefore generalize related results on resonance graphs of benzenoid graphs, catacondensed even ring systems, as well as 2-connected outerplane bipartite graphs. Firstly, we prove that if $G$ is a plane elementary bipartite graph other than $K_2$, then the resonance graph $R(G)$ is a daisy cube if and only if the Fries number of $G$ equals the number of finite faces of $G$, which in turn is equivalent to $G$ being homeomorphically peripheral color alternating. Next, we extend the above characterization from plane elementary bipartite graphs to all plane bipartite graphs and show that the resonance graph of a plane bipartite graph $G$ is a daisy cube if and only if $G$ is weakly elementary bipartite and every elementary component of $G$ other than $K_2$ is homeomorphically peripheral color alternating. Along the way, we prove that a Cartesian product graph is a daisy cube if and only if all of its nontrivial factors are daisy cubes

Outerplane bipartite graphs with isomorphic resonance graphs

We present novel results related to isomorphic resonance graphs of 2-connected outerplane bipartite graphs. As the main result, we provide a structure characterization for 2-connected outerplane bipartite graphs with isomorphic resonance graphs. Moreover, two additional characterizations are expressed in terms of resonance digraphs and via local structures of inner duals of 2-connected outerplane bipartite graphs, respectively