Improved bounds for the largest eigenvalue of trees
Improved bounds for the largest eigenvalue of trees
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DOI：
10.1016/j.laa.2005.02.023
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发表时间：
2005-07
影响因子：
1.1
通讯作者：
O. Rojo
中科院分区：
文献类型：
--
作者：
O. Rojo
设T是一棵顶点集为V的树，v∈V的度记为v.设Δ=max{dv：v∈V}。设u∈V使得du=Δ。设k=eu+1，其中eu是u的偏心率。对于j= 1，2，.，k −2，我们证明了其中μ1（T）和λ1（T）分别是T的Laplacian矩阵和邻接矩阵的最大特征值.这些界给出了比[D. Stevanović，Linear Algebra Appl.360（2003）35-42]，除非δ1=Δ。
Let T be a tree with vertex set V. Let dvdenotes the degree of v∈V. Let Δ=max{dv:v∈V}. Let u∈V such that du=Δ. Let k=eu+1 where euis the excentricity of u. For j=1,2,…,k−2, letWe prove thatandwhere μ1(T) and λ1(T) are the largest eigenvalue of the Laplacian matrix and adjacency matrix of T, respectively. These bounds give better results than those obtained in [D. Stevanović, Linear Algebra Appl. 360 (2003) 35–42] except if δ1=Δ.