第二个大根不超过2^(1/2)的树

On Trees Whose Second Largest Eigenvalue Does Not Exceed 2^(1/2)

1982 年Cvetkovic D 提出“求出图的第二大根λ2( G) ≤1 的所有图”这一问题,1993 年,Hong Y 和Cao D 给出了λ2(G)≤13 的所有图,紧接着Miroslav P给出了λ2( G) ≤2 - 1 的所有图,但对Cvetkovic D 的问题的解决还需进一步的努力。1998 年,作者给出了第二个大根不超过1 的所有树。该文分别给出了第二个大根小于2 的所有树和第二个大根等于2 的所有树。

In 1982, Cvetkovic D posed the problem of characterizing graphs with the second largest eigenvalue not greater than 1. Cao D and Hong Y determined graphs without isolated vertices with the property 0<λ 2(G)≤13 . In 1993, Miroslav P gave all grahps with the property λ 2(G)≤2-1 . There are great difficulty to solute the problem of Cvetkovic D. In 1998, We obtained all of trees whose second largest eigenvalue is not greater than 1. All of trees whose second largest eigenvalue is not greater than 2 are presented in this paper.