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) |
|---|---|
| Pages (from-to) | 264-268 |
| Number of pages | 5 |
| Journal | Discrete Applied Mathematics |
| Volume | 258 |
| DOIs | |
| State | Published - Apr 15 2019 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
Cite this
}
A characterization of the resonance graph of an outerplane bipartite graph. / Che, Zhongyuan.
In: Discrete Applied Mathematics, Vol. 258, 15.04.2019, p. 264-268.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).
UR - http://www.scopus.com/inward/record.url?scp=85058778905&partnerID=8YFLogxK
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 -