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On Graphs with Distinct Eigenvalues

Author: MaZhiHui
Tutor: HuangQiongXiang
School: Xinjiang University
Course: Applied Mathematics
Keywords: Eigenvalues Characteristic polynomial Eigenvector Diameter
CLC: O157.5
Type: Master's thesis
Year: 2011
Downloads: 17
Quote: 0
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Abstract


Figure eigenvalues ??and algebraic graph theory is a cross-cutting area of ??research, is a branch of algebraic graph theory in 1974 , F. Harary and AJ Schwenk in the literature [ 1 ] proposed an open question: which graphs are the eigenvalues different from each other ? but unfortunately the conclusions in this regard so far little paper mainly with characteristic polynomial and interlacing theorems characterize diameter d (G) = n - 2 eigenvalues ??different from each diagram , the main contents are as follows : In the Chapter Introduction , we give the definition of characteristic values ??, symbols and notations , and recalled the eigenvalues ??of history and current situation . cited predecessors about k distinct eigenvalues ??research. No. Chapter II is divided into three , section describes some of the evidence in this article are some of the important needs lemma, corollary section II gives the diameter d (G) = n - 2 graphs and diagrams based on parity the graph G ( see Figure 2 ) into two groups: the first two types referred to as : D n-2 0 = {P n-1 k 1 , P n-1 k, k 2 | 1 ≤ k ≤ n - 3}, then the two types referred to as : D n-2 1 = {P n-1 k, k 1 (1 ≤ k ≤ n - 2), P n-1 k, k 1, k 2 (1 ≤ k ≤ n -3}. III completely characterize the D n-2 0 in Figure mutually different eigenvalues ??third chapter we first introduced the staggered theorem, and the use of staggered theorem and eigenvectors of the matrix portion portrayed in D n-2 1 eigenvalues ??different from each other in Fig. Let G be a n vertices , diameter d (G) = n-2 non- bipartite graph ( Figure 4 (a), (b) below) , where n ≥ 4. if 3 (?) n, then G has n eigenvalues ??different from each other .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
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