| 关于图谱的几个定理 |
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| 引用本文： | 陈建生. 关于图谱的几个定理[J]. 华中科技大学学报(自然科学版), 1992, 0(2) |
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| 作者姓名： | 陈建生 |
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| 作者单位： | 华中理工大学数学系 |
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| 摘 要： | 本文给出了边独立数为q的树(或森林)的第k大正特征值的下界,并且证明这个下界在很多情况下是最好可能的;又给出了一种使得具有完美对集的树最小正特征值递减的变形,从而为一个关于最小正特征值的Sharp下界的猜想给出了一种更有应用前景的新证明.
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| 关 键 词： | 图谱 第k大特征值 界 |
Some Theorems on the Spectra of Graphs |
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| Chen Jiansheng. Some Theorems on the Spectra of Graphs[J]. JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE, 1992, 0(2) |
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| Authors: | Chen Jiansheng |
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| Affiliation: | Chen Jiansheng |
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| Abstract: | Let k be the kth largest eigenvalue of a tree (or a forest) with an edge independence number of q. It is proved that 2cos. where and this lower bound is thebest possible for q=l,2,...,[i/2] (mod i + 1). A distortion by which the least positive eigenvalue of a tree having perfect matching decreases succe ssively is obtained and a new proof having better prospects for the application of a conjecture about the sharp lower bound of the least positive eigenvalue is given. |
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| Keywords: | spectra of graphs the kth largest eigenvalue bound |
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