On the Spectrum of Trees

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7952

Title:	On the Spectrum of Trees
Authors:	許立成;Li-Cheng Hsu
Contributors:	數學研究所
Keywords:	Bethe樹;$v$-symmetric eigenvector;symmetric eigenvector;skew symmetric vector;symmetric vector;$i$-level subtree of Bkn;Bethe tree;$i$-level set
Date:	2009-03-26
Issue Date:	2009-09-22 11:10:00 (UTC+8)
Publisher:	國立中央大學圖書館
Abstract:	在1984年，Godsil 定義了 Bethe樹圖B(k,n)，並求出其譜半徑 ho的上界滿足 $rho<2sqrt{k}$。在我們這篇論文中，我們找出Bethe樹圖的譜，利用此結論，我們又證明了任一樹圖T 的譜半徑滿足 $$sqrt{Delta}leq ho< min{2sqrt{Delta-1}cos{(frac{pi}{D+2})},2sqrt{Delta}cos{(frac{pi}{r+2})}},$$ 其中D，r，Delta分別為此樹圖的直徑，半徑，與最大度數。此下界等號成立只發生在當T為完全二部圖K_{1,Delta}時。 In 1984, Godsil defined the Bethe tree $B(k,n)$ and showed the spectral radius $ ho$ of $B(k,n)$ satisfies $ ho<2sqrt{k}$. In this thesis, we find the spectrum of $B(k,n)$. With this spectrum, we also show the spectral radius $ ho$ of a tree $T$ satisfies $$sqrt{Delta}leq ho< min{2sqrt{Delta-1}cos{(frac{pi}{D+2})},2sqrt{Delta}cos{(frac{pi}{r+2})}},$$ where $D$,$r$,$Delta$ are the diameter, radius, and the maximum degree of $T$ respectively. The equality of lower bound holds only when $T=K_{1,Delta}$.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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