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
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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). |
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