星型树和双星树的谱半径的界

针对星型树和双星树,通过删除割点、割边的图运算方法,利用特征多项式根与系数的关系先给出了谱半径的上界,然后由已知的结论推出广义星型树图谱半径的界,最后从改变最大度和第二大度出发,通过剖分广义星型树的内部路以及外部路,得到谱半径的变化不超过1.

Bounds for the Spectral Radii of Starlike and Double-Starlike Trees

For starlike and double-starlike trees, by deleting cut points and cut edges, the upper bound of spectral radius is given from the relationship between the root of the characteristic polynomial and the coefficient. Then, the bound of spectral radius of the generalized starlike tree is derived from known conclusions. Finally, starting from changing the maximum and the second maximum, the inner path and the outer path of the generalized starlike tree are divided, and the change of the spectral radius is shown to be less than 1.