有关Seidel整树的一些结果

Some Results on the Seidel Integral Trees

本文通过对直径分别为2、3和4的树图的Seidel特征多项式和特征根进行研究,得出以下结论:(1)直径为2的树都是Seidel整树;(2)给出了直径为3的树是Seidel整树的充分必要条件,并从中找出了一些特殊的Seidel整树的情形;(3)找出了一些特殊的直径为4的Seidel整树.

In this paper, by investigating the Seidel characteristic polynomial and Seidel characteristic eigenvalues of trees for diameter 2.3 and 4 respectively, we obtain the following conclusions： （1）All trees for diameter 2 are Seidel integral trees; （2） The necessary and sufficient condition for the trees for diameter 3 to be Seidel integral trees is given and finding some particular Seidel integral trees for diameter 3; （3） we find out some particular Seidel integral trees for diameter 4.