论文标题
扎根树的分配理性功能
Assigned rational functions of a rooted tree
论文作者
论文摘要
我们研究了根树的光谱特性，目的是改善目前现有的涉及此问题的结果。分配的有理函数的概念是针对根部树的每个顶点的。之后，给出了两个数学公式，其中显示了如何将邻接和拉普拉斯矩阵的特征多项式表示为上述有理函数的产物。为了证明其一般用例情况，所获得的公式随后在平衡的树上实施，特别关注伯特树。最后，使用了一些先前派生的结果，以构建树木合并过程，该过程保留了所有起始树的光谱。
We investigate the spectral properties of rooted trees with the intention of improving the currently existing results that deal with this matter. The concept of an assigned rational function is recursively defined for each vertex of a rooted tree. Afterwards, two mathematical formulas are given which show how the characteristic polynomials of the adjacency and Laplacian matrix can be represented as products of the aforementioned rational functions. In order to demonstrate their general use case scenario, the obtained formulas are subsequently implemented on balanced trees, with a special focus on the Bethe trees. In the end, some of the previously derived results are used in order to construct a tree merging procedure which preserves the spectra of all of the starting trees.
