### Abstract

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).

Original language | English (US) |
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Pages (from-to) | 264-268 |

Number of pages | 5 |

Journal | Discrete Applied Mathematics |

Volume | 258 |

DOIs | |

State | Published - Apr 15 2019 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

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**A characterization of the resonance graph of an outerplane bipartite graph.** / Che, Zhongyuan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A characterization of the resonance graph of an outerplane bipartite graph

AU - Che, Zhongyuan

PY - 2019/4/15

Y1 - 2019/4/15

N2 - 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).

AB - 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).

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UR - http://www.scopus.com/inward/citedby.url?scp=85058778905&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2018.11.032

DO - 10.1016/j.dam.2018.11.032

M3 - Article

VL - 258

SP - 264

EP - 268

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -