| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 許立成 | zh_TW |
| DC.creator | Li-Cheng Hsu | en_US |
| dc.date.accessioned | 2009-7-23T07:39:07Z | |
| dc.date.available | 2009-7-23T07:39:07Z | |
| dc.date.issued | 2009 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=952201029 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.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。
| zh_TW |
| dc.description.abstract | 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 $T=K_{1,Delta}$.
| en_US |
| DC.subject | Bethe樹 | zh_TW |
| DC.subject | $v$-symmetric eigenvector | en_US |
| DC.subject | symmetric eigenvector | en_US |
| DC.subject | skew symmetric vector | en_US |
| DC.subject | symmetric vector | en_US |
| DC.subject | $i$-level subtree of Bkn | en_US |
| DC.subject | Bethe tree | en_US |
| DC.subject | $i$-level set | en_US |
| DC.title | On the Spectrum of Trees | en_US |
| dc.language.iso | en_US | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |