TY - JOUR

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

AU - Che, Zhongyuan

N1 - Publisher Copyright:
© 2018 Elsevier B.V.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

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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U2 - 10.1016/j.dam.2018.11.032

DO - 10.1016/j.dam.2018.11.032

M3 - Article

AN - SCOPUS:85058778905

VL - 258

SP - 264

EP - 268

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -