| 由谱半径给树排序 |
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| 引用本文： | 蔡菁,王国平.由谱半径给树排序[J].新疆师范大学学报(自然科学版),2008,27(1):1-4. |
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| 作者姓名： | 蔡菁 王国平 |
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| 作者单位： | 新疆师范大学,数理信息学院,新疆,乌鲁木齐,830054 |
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| 摘 要： | 设△（T）和λ1（T）分别表示树T的最大度和谱半径，Tn表示有n个点的树且Tn^（△）=（T∈Tn｜△（T）=△}，文章根据树的谱半径给Tn^n-6（n≥18）中的树进行了排序并将结果扩大到第78棵树。
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| 关 键 词： | 树 特征多项式 谱半径 排序 |
| 文章编号： | 1008-9659-(2008)-01-0001-03 |
| 修稿时间： | 2007年10月27 |
Ordering Trees by Their Largest Eigenvalues |
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| CAI Jing,WANG Guoping.Ordering Trees by Their Largest Eigenvalues[J].Journal of Xinjiang Normal University(Natural Sciences Edition),2008,27(1):1-4. |
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| Authors: | CAI Jing WANG Guoping |
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| Institution: | (School of Maths- physics and Information Science, Xinjiang Normal University, Urumqi Xinjiang 830054) |
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| Abstract: | 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. |
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| Keywords: | Tree characteristic polynomial spectral radius ordering |
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