I-hedrite图平面嵌入的唯一性

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.

The Uniqueness of Embedded I-hedrite in the Plane

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.