On the spectra of nonsymmetric Laplacian matrices

Linear Algebra and Its Applications

Volumn 399, Issue 1-3, 2005, Pages 157-168

  Agaev, Rafig ^a   Chebotarev, Pavel ^a  

^a TRAPEZNIKOV INSTITUTE OF CONTROL SCIENCES   (Russian Federation)

Author keywords

Forest dimension of digraph; Laplacian matrix; Laplacian spectrum of graph; Stochastic matrix; Weighted directed graph

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; GRAPH THEORY; LAPLACE TRANSFORMS; RANDOM PROCESSES; SPECTRUM ANALYSIS; STANDARDS;

FOREST DIMENSION OF DIGRAPH; LAPLACIAN MATRIX; LAPLACIAN SPECTRUM OF GRAPH; STOCHASTIC MATRIX; WEIGHTED DIRECTED GRAPH;

MATRIX ALGEBRA;

EID: 14644405640     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2004.09.003     Document Type: Conference Paper

References (21)

1. W.N. Anderson Jr., and T.D. Morley Eigenvalues of the Laplacian of a graph Linear and Multilinear Algebra 18 1985 141 145
2. A. Berman, and R.J. Plemmons Nonnegative Matrices in the Mathematical Sciences 1979 Academic Press New York (second ed., SIAM, 1995).
3. S. Chaiken A combinatorial proof of the all minors matrix tree theorem SIAM J. Algebraic Discrete Methods 3 1982 319 329
4. P. Chebotarev, and R. Agaev Forest matrices around the Laplacian matrix Linear Algebra Appl. 356 2002 253 274
5. W.K. Chen Applied Graph Theory, Graphs and Electrical Networks 1976. North-Holland Amsterdam
6. F.R.K. Chung Spectral Graph Theory 1997. American Mathematical Society Providence, RI
7. N. Dmitriev, and E. Dynkin On the characteristic numbers of a stochastic matrix C. R. (Doklady) Acad. Sci. URSS 49 3 1945 159 162
8. N. Dmitriev, and E. Dynkin On characteristic roots of stochastic matrices Izv. Akad. Nauk SSSR (Bull. Acad. Sci. USSR) Ser. Mat. 10 1946 167 184
9. J.A. Fax, R.M. Murray, Graph Laplacians and stabilization of vehicle formations, in: Proceedings of the 15th IFAC Congress, Barcelona, Spain, July 2002
10. M. Fiedler, and J. Sedláček O W-basích orientovaných grafů Časopis Pěst. Mat. 83 1958 214 225
11. R. Grone, R. Merris, and V.S. Sunder The Laplacian spectrum of a graph SIAM J. Matrix Anal. Appl. 11 1990 218 238
12. R. Grone, and R. Merris The Laplacian spectrum of a graph II SIAM J. Discrete Math. 7 1994 221 229
13. R.A. Horn, and C.R. Johnson Matrix Analysis 1986. Cambridge University Press Cambridge
14. A.K. Kel'mans The number of trees in a graph I Autom. Remote Control 26 1965 2118 2129
15. A.K. Kel'mans The number of trees in a graph II Autom. Remote Control 27 1966 233 241
16. A.K. Kelmans, and V.M. Chelnokov A certain polynomial of a graph and graphs with an extremal number of trees J. Comb. Theory, Ser. B 16 1974 197 214
17. R. Merris Laplacian matrices of graphs: a survey Linear Algebra Appl. 197-198 1994 143 176
18. R. Merris A survey of graph Laplacians Linear and Multilinear Algebra 39 1995 19 31
19. B. Mohar Laplace eigenvalues of graphs-a survey Discrete Math. 109 1992 171 183
20. G. Pick Uber die Wurzeln der charakterististischen Gleichungen von Schwingungsproblemen Z. Angew. Math. Mech. 2 1922 353 357
21. W.T. Tutte Graph Theory 1984 Addison-Wesley Reading, MA