樹圖最大特徵值的討論

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蔡銘璟(Min-Ching Tsai) 查詢紙本館藏

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論文名稱

樹圖最大特徵值的討論
(On the spectral radius of trees)

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★ On the Spectrum of Trees

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摘要(中)

我們討論根樹圖的譜值,並得到一些分類的結果

摘要(英)

We discuss the spectrum of balanced rooted tree

關鍵字(中)

★ 樹圖
★ 特徵值
★ 譜值

關鍵字(英)

★ Bethe tree
★ balanced rooted tree
★ spectrum
★ spectral radius

論文目次

Chapter 0 Historical review and overview of the thesis 1
0.1 Historical review.............................1
0.2 Overview of the thesis........................2
Chapter 1 Preliminaries 3
1.1 Basic definitions on graph theory.............3
1.2 Preliminaries on the eigenvalue problem.......5
Chapter 2 Computation of the graph spectrum 8
2.1 Equitable partitions..........................8
2.2 Graphs with recursive structure..............11
2.3 Graph defined by some algebraic identity.....12
2.4 Eigenvector can be regarded as a harmonic function.....................................13
Chapter 3 Main results 15
3.1 Bethe tree B(k, n) and balanced rooted trees R(k_1,...,k_n)...............................15
3.2 Spectrum of R(k_1,...,k_n)...................16
3.3 The spectral radius of the long leg spider
Sp(k, n).....................................25
3.4 The spectral radius of the subgraphs of R(k,1)...............................27
Chapter 4 Possible Future Works 29
References 30

參考文獻

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D-bounded Distance-Regular Graphs, Thesis of master, 2008.

指導教授

黃華民(Hua-Min Huang)

審核日期

2009-6-30

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