摘要
设Δ(T)和λ1(T)分别表示树Τ的最大度和谱半径,Tn表示有n个点的树且T(nΔ)={T∈Tn|Δ(T)=Δ},文章根据树的谱半径给Tnn-6(n≥18)中的树进行了排序并将结果扩大到第78棵树。
Let △(T) and λ(T) denote the maximum degree and the largest eigenvalue of a tree T , respectively.
Let Tn be the set of trees on n vertices , and Tn^(△)=(T∈Tn|△(T)=△}. In the present paper , among the trees in Tn^(△)(n≥4), we characterize the tree which alone maximizes the largest eigenvalue when [n-2/2≤△≤n-1. Furthermore, it is proved that, for two trees T1 and T2 in Tn (n≥4), if △(T1)≥[2n/3]-1 and △(T1)〉△(T2),then λ1 (T1))〉λ1 (T2). By applying this result, we extend the order of trees in T. by their largest eigenvalue to the 79th tree when n ≥18.
出处
《新疆师范大学学报(自然科学版)》
2008年第1期1-3,22,共4页
Journal of Xinjiang Normal University(Natural Sciences Edition)
关键词
树
特征多项式
谱半径
排序
Tree
characteristic polynomial
spectral radius
ordering