Dissertation > Excellent graduate degree dissertation topics show

Some Graphs are Determined by Their Spectra

Author: MengYao
Tutor: ShuJinLong
School: East China Normal University
Course: Operational Research and Cybernetics
Keywords: θ-graph Eigenvalues Laplacian spectrum DS-graph Cospectral graphs
CLC: O157.5
Type: Master's thesis
Year: 2010
Downloads: 32
Quote: 0
Read: Download Dissertation

Abstract


The theory of graph spectra is an active and important area in graph theory. There are extensive applications in the fields of quantum chemistry, statistical mechanics, computer science, communication networks and infor-mation science. In the theory of graph spectra, there are various matrices that are naturally associated with a graph, such as the adjacency matrix, the Laplacian matrix, the incidence matrix and so on. Among the above mentioned matrices of graphs, the most important two are the adjacency matrices and the Laplacian matrices of graphs. This thesis mainly researchs the hot problem of Laplacian spectral characterization through investigates Laplacian matrices. In [1], F. Ramezani et al. proved that anyθ-graph is determined by the adjacency spectrum (the multiset of eigenvalues) except possibly when it contains a unique 4-cycle. On the basis of their conclusions, we researchs the Laplacian spectral characterization ofθ-graph, the main conclusions are as follows:1. We have proved thatθ-graphθs1,s2,s3(|si—sj|≤2,1≤i≤j≤3) is determined by its Laplacian spectrum;2. We have proved thatθ-graph of girth 3 is determined by its Lapla-cian spectrum;3. We have proved thatθ-graph of girth 4 is determined by its Lapla-cian spectrum;4. We have proved thatθ-graph ofθ0,u,v(u+v=1(mod 2)) is deter- mined by its Laplacian spectrum;5. On the basis of above conclusions, we give a conjecture on Laplacian spectral characterization ofθ-graph.

Related Dissertations

  1. On the Spectrum and Laplacian Spectrum of Some Special Hypercubes,O157.5
  2. The Game Coloring and Adjacent Strong Edge Coloring of Some Graphs,O157.5
  3. Hamilton imaginary eigenvalues ??of the matrix method for solving the rapid,O151.21
  4. On Graphs Determined by Their Spectrum and Angle,O157.5
  5. Spectral Characterization of Several Classes of Graphs,O157.5
  6. Laplace spectrum and Figure adjacency spectrum,O157.5
  7. Full binary tree Laplacian Eigenvalues ??Merris Index,O157.5
  8. On Graphs Determined by Their Spectrum,O157.5
  9. Resistance Distance and Kirchhoff Index in Graphs,O157.5
  10. On the Adjacent Vertex Distinguishing Total Coloring of Some Graphs,O157.5
  11. The Sum of All Distances and the Average Distance in a Connected Graph,O157.5
  12. The matrix determinant Inequality inverse eigenvalue problem,O151.25
  13. The Theory of Correspondence Analysis and Its Application in the Simplification of Sampling Questionnaires,O29
  14. Estimating the vector hydrophone goal position,U666.7
  15. Dynamic Study of Periodic Time-Varying Cam-Follower Systems,TH132.47
  16. The Completeness of Eigenfuction System for Two Regular 2×2 Sturm-Liouville Problems,O175
  17. An Improved Algebraic Method for Computing Eigensolution Sensitivity of Asymmetric Damped Systems,TB126
  18. Research on Furnace Outfire Judgment Based on Support Vector Machine,TP274
  19. Computing Vibrational and Vibrational-Rotational Energy Eigenvalues and Frank-Condon Factors of ～7Li2 by Finite Difference Method,O431.2
  20. Schr (?) Dinger operator the two eigenvalue spacing estimated transfer boundary conditions differential operator of self-adjoint sub sex,O177

CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory
© 2012 www.DissertationTopic.Net  Mobile