TY - JOUR
T1 - A characterization of the resonance graph of an outerplane bipartite graph
AU - Che, Zhongyuan
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
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
SN - 0166-218X
VL - 258
SP - 264
EP - 268
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -