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研究生： 蔡銘璟
Min-Ching Tsai
論文名稱： 樹圖最大特徵值的討論
On the spectral radius of trees
指導教授： 黃華民
Hua-Min Huang
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 97
語文別： 英文
論文頁數： 36
中文關鍵詞： 樹圖 、特徵值 、譜值
外文關鍵詞： Bethe tree, balanced rooted tree, spectrum, spectral radius
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    • 我們討論根樹圖的譜值,並得到一些分類的結果

    We discuss the spectrum of balanced rooted tree

    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

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    Combin. Theory Ser. B 81 (2001) 177-183.
    [9] J.L. Shu, Y. Wu, Sharp upper bounds on the spectral radius of graphs, Linear Algebra Appl. 377 (2004) 241–248.
    [10] D. Cao, Bounds of eigenvalues and chramatic numbers, Linear Algebra Appl. 270 (1998) 1–13.
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    [12] L. Collatz, U. Sinogowitz, Spektren Endlicher Grafen, Abh. Math. Sem. Univ. Hamburg 21 (1957) 63-77.
    [13] R. A. Horn and C. R. Johnson, Matrix analysis, Cambridge, preprint.
    [14] Norman Biggs, Algebraic graph theory, Cambridge, Second Edition 1993.
    [15] Douglas B. West, Introduction to Graph Theory, Prentice Hall, Second Edition 2001
    [16] T.C. Hu, Combinatorial Algorithms , Addison-Wesley, 1982.
    [17] J. M. Aldous and R. J. Wilson, Graphs and applications, Springer, 2001.
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    [20] Li-Cheng Hsu, On the Spectrum of Trees, Thesis of master, 2009.
    [21] Ya-Jung Tseng, Constructing Strongly Regular Graphs from
    D-bounded Distance-Regular Graphs, Thesis of master, 2008.

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