以对轮图为缩影图式流形的同胚类数

The Homeomorphic Class number of Graphlike Manifold with Contraction Round Diagrams

摘要: 对于某些自然数n，通过分类法可以得出以对轮图W_n 为缩影的所有图式流形W_n^*的同胚类的类数，并且用Matlab软件算出W_n^*中每个图式流形的伴随矩阵的不同特征多项式个数，得出W_n^*同胚类数的下界。对于所有的自然数n，利用Burnside引理给出了求W_n^*的同胚类数的上界的一个方法。

Abstract: This article obtains the number of homeomorphic class of W_n^*  by means of classification for some natural numbers n. It uses Matlab to compute the adjoint matrix of  W_n^* and calculate the number of characteristic polynomial, and then get the lower bound of the number of homeomorphic class of  W_n^*. For all natural numbers, it puts forward a method to calculate the upper bound of the number of homeomorphic class by using Burnside’s lemma.