A characterization of 1-cycle resonant graphs among bipartite 2-connected plane graphs

Klavar S.; Salem K.

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A characterization of 1-cycle resonant graphs among bipartite 2-connected plane graphs

机译：二部2连通平面图之间的1周期共振图的特征

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It is proved that a bipartite 2-connected plane graph in which the common boundary of adjacent faces is a simple curve is 1-cycle resonant if and only if the outer face of G is alternating and each inner vertex has degree two. This extends a result from [X. Guo, F. Zhang, k-cycle resonant graphs, Discrete Math. 135 (1994) 11320] that a hexagonal system is 1-cycle resonant if and only if it is catacondensed.

机译：证明了当且仅当G的外表面是交替的并且每个内部顶点的度数为2时，相邻面的公共边界为简单曲线的二部2连通平面图才是1周期共振。这扩展了[X.郭，F。张，k周期共振图，离散数学。 135（1994）11320]认为，当且仅当六方体系被催化缩合时，它才是一周期共振。

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《Discrete Applied Mathematics》 |2012年第8期|共4页
作者
Klavar S.; Salem K.;
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正文语种 eng
中图分类离散数学;
关键词
1-cycle resonant graph; Alternating cycle; Bipartite plane graph; Hexagonal system;

机译：一周期共振图;交替周期;二分平面图;六边形系统;

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专利

1. A characterization of 1-cycle resonant graphs among bipartite 2-connected plane graphs [J] . Klavar S., Salem K. Discrete Applied Mathematics . 2012,第7a8期

机译：二部2连通平面图之间的1周期共振图的特征
2. Reducible chains of planar 1-cycle resonant graphs [J] . Xiaofeng Guo, Fuji Zhang Discrete mathematics . 2004,第1a3期

机译：平面1周期共振图的可约链。
3. The Endomorphism Type of Certain Bipartite Graphs and a Characterization of Projective Planes [J] . K?hl R., M?ser K., van Maldeghem H. Graphs and combinatorics . 2013,第2期

机译：某些二部图的内胚类型和投影平面的刻画
4. A Simple Linear Time Algorithm for Finding Even Triangulations of 2-Connected Bipartite Plane Graphs [C] . Huaming Zhang, Xin He 10th Annual European Symposium on Algorithms - ESA 2002, Sep 17-21, 2002, Rome, Italy . 2002

机译：一种简单的线性时间算法，用于查找2连通二分平面图的偶三角剖分
5. Electrochemical deposition of silver and platinum nano-crystallites on the atomically smooth graphite basal plane: Characterization, particle size control, and chemical applications. [D] . Zoval, James Vincent. 1996

机译：银和铂纳米微晶在原子光滑的石墨基面上的电化学沉积：表征，粒度控制和化学应用。
6. In-Plane Resonant Nano-Electro-Mechanical Sensors: A Comprehensive Study on Design Fabrication and Characterization Challenges [O] . Faezeh Arab Hassani, Yoshishige Tsuchiya, Hiroshi Mizuta 2013

机译：平面共振纳米机电传感器：设计制造和表征挑战的综合研究
7. Reducible chains of planar 1-cycle resonant graphs [O] . Guo Xiaofeng, Zhang Fuji 2004

机译：平面1周期共振图的可约链。

A characterization of 1-cycle resonant graphs among bipartite 2-connected plane graphs

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