I-hedrite图平面嵌入的唯一性

林跃峰

数学学报 ›› 2017, Vol. 60 ›› Issue (6) : 919-930.

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数学学报 ›› 2017, Vol. 60 ›› Issue (6) : 919-930. DOI: 10.12386/A2017sxxb0079
论文

I-hedrite图平面嵌入的唯一性

    林跃峰
作者信息 +

The Uniqueness of Embedded I-hedrite in the Plane

    Yue Feng LIN
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文章历史 +

摘要

本文研究每一个面圈的圈长仅为2,3或4的无割点的4-正则连通平面图,称之为I-hedrite图.证明在相等意义上,I-hedrite图的平面嵌入是唯一的.这个唯一性结论意味着,两个i-hedrite图(即每一个面的度仅为2,3或4的4-正则连通平图)是相等的当且仅当它们是同构的,从而解决了i-hedrite图的同构构造在相等意义上的唯一性问题.

Abstract

We study any 4-valent connected planar graph without cut vertices whose facial cycle lengths are of 2, 3 or 4 only, called them I-hedrites. We prove that in the equal sense every I-hedrite is uniquely embedded in the plane. This uniqueness conclusion means that any two i-hedrites (i.e. 4-valent connected plane graph whose faces are 2-, 3-and 4-gons only) are equal if and only if they are isomorphic. The result solves the problem of certainty in isomorphism structure of i-hedrite in the equal sense.

关键词

平面嵌入 / 唯一性 / I-hedrite图 / i-hedrite图 / 同构 / 相等

Key words

planar embedding / uniqueness / I-hedrite / i-hedrite / isomorphism / equal

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林跃峰. I-hedrite图平面嵌入的唯一性. 数学学报, 2017, 60(6): 919-930 https://doi.org/10.12386/A2017sxxb0079
Yue Feng LIN. The Uniqueness of Embedded I-hedrite in the Plane. Acta Mathematica Sinica, Chinese Series, 2017, 60(6): 919-930 https://doi.org/10.12386/A2017sxxb0079

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