Outerplane bipartite graphs with isomorphic resonance graphs. (English) Zbl 1529.05075
Summary: 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. Three additional characterizations are expressed in terms of resonance digraphs, via local structures of inner duals, as well as using distributive lattices on the set of order ideals of posets defined on inner faces of 2-connected outerplane bipartite graphs.
MSC:
| 05C20 | Directed graphs (digraphs), tournaments |
| 05C60 | Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) |
| 05C92 | Chemical graph theory |
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
Keywords:
distributive lattice; inner dual; isomorphic resonance graphs; isomorphic resonance digraphs; order ideal; 2-connected outerplane bipartite graphReferences:
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