Ordering trees by their largest eigenvalues

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	Ordering trees by their largest eigenvalues
	Lin, W. S. ; Guo, X. F. ; Guo XF(郭晓峰)
刊名	http://dx.doi.org/10.1016/j.laa.2006.02.035
	2006-10-15
关键词	BOUNDS
英文摘要	Let Delta(T) and lambda(1)(T) denote the maximum degree and the largest eigenvalue of a tree T, respectively. Let T-n be the set of trees on n vertices, and T-n((Delta)) = {T is an element of T-n vertical bar Delta(T) = Delta}. In the present paper, among the trees in T-n((Delta)) (n >= 4), we characterize the tree which alone minimizes the largest eigenvalue, as well as the tree which alone maximizes the largest eigenvalue when [(n-2)/(2)] <= Delta <= n-1. Furthermore, it is proved that, for two trees T-1 and T-2 in T-n (n >= 4), if Delta(T-1) >= [(2n)/(3)]-1 and Delta(T-1) > Delta(T-2), then lambda(1)(T-1) > lambda(1)(T-2). By applying this result, we extend the order of trees in T-n by their largest eigenvalues to the 13th tree when n >= 12. This extends the results of Hofmeister [Linear Algebra Appl. 260 (1997) 43] and Chang et al. [Linear Algebra Appl. 370 (2003) 175]. (c) 2006 Elsevier Inc. All rights reserved.
语种	英语
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/66789]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Lin, W. S.,Guo, X. F.,Guo XF. Ordering trees by their largest eigenvalues[J]. http://dx.doi.org/10.1016/j.laa.2006.02.035,2006.
APA	Lin, W. S.,Guo, X. F.,&郭晓峰.(2006).Ordering trees by their largest eigenvalues.http://dx.doi.org/10.1016/j.laa.2006.02.035.
MLA	Lin, W. S.,et al."Ordering trees by their largest eigenvalues".http://dx.doi.org/10.1016/j.laa.2006.02.035 (2006).