谱半径为4的整树

The integral trees with index 4

整图刻画的问题是学术届公认的十分难的问题,本文利用图的特征多项式、谱与图的直径的关系等,刻画了谱半径为4,谱λ?3的所有整树,这样的树有且仅有18种。

Integral graphs are very difficult to be found. In this paper, by the characteristic polynomials and the relations of spectrum and diameter of graph, all integral trees with index 4 and avoiding 3 in the spectral are determined, such trees have only 18 species.