A characterization of the resonance graph of an outerplane bipartite graph

Let G be a 2-connected outerplane bipartite graph and R(G) be its resonance graph. It is known that R(G) is a median graph. Assume that s is a reducible face of G and H is the subgraph of G obtained by removing all internal vertices (if exist) and edges on the common periphery of s and G. We show th...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2019-04, Vol.258, p.264-268
Main Author: Che, Zhongyuan
Format: Article
Language:English
Subjects:
[formula omitted]-transformation graph
Apexes
Djoković–Winkler relation [formula omitted]
Graph theory
Graphs
Median graph
Outerplane bipartite graph
Peripheral convex expansion
Reducible face
Resonance graph
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Summary:Let G be a 2-connected outerplane bipartite graph and R(G) be its resonance graph. It is known that R(G) is a median graph. Assume that s is a reducible face of G and H is the subgraph of G obtained by removing all internal vertices (if exist) and edges on the common periphery of s and G. We show that R(G) can be obtained from R(H) by a peripheral convex expansion. As an application, we prove that Θ(R(G)) is a tree and isomorphic to the inner dual of G, where Θ(R(G)) is the induced graph on the Djoković–Winkler relation Θ-classes of R(G).
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2018.11.032