Laplacian graph eigenvectors

Linear Algebra and Its Applications

Volumn 278, Issue 1-3, 1998, Pages 221-236

  Merris, Russell ^a  

^a CALIFORNIA STATE UNIVERSITY   (United States)

Author keywords

Algebraic connectivity; Decomposable graph; Faria vector; Fiedler vector; Graph join; Graph product; Graph spectra; Isospectral graphs; Kronecker product; Laplacian integral graph; Spectrally unique graph; Threshold graph

Indexed keywords

EID: 11544285071     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(97)10080-5     Document Type: Article

References (21)

1. W.N. Anderson, T.D. Morley, Eigenvalues of the Laplacian of a graph, Linear and Multilinear Algebra 18 (1985) 141-145.
2. S.T. Barnard, A. Pothen, H. Simon, A spectral algorithm for envelope reduction of sparse matrices, J. Numer. Linear Algebra Appl. 2 (1995) 317-334.
3. P. Botti, R. Merris, Almost all trees share a complete set of immanantal polynomials, J. Graph Theory 17 (1993) 467-476.
4. F.C. Bussemaker, D.M. Cvetković, There are exactly 13 connected, cubic, integral graphs, Univ. Beograd Publ. Elektrotehn. Fak., Ser. Mat. Fiz. 544-576 (1976) 43-48.
5. D.M. Cvetković, M. Doob, H. Sachs, Spectra of Graphs, 3rd ed., Johann Ambrosius, Heidelberg, 1995.
6. D.M. Cvetković, P. Rowlinson, S. Simić, Eigenspaces of Graphs, Encyclopedia of Math. Appl. 66, Cambridge Univ. Press, Cambridge, 1997.
7. I. Faria, Multiplicity of integer roots of polynomials of graphs, Linear Algebra Appl. 229 (1995) 15-35.
8. M. Fiedler, Algebraic connectivity of graphs, Czech. Math. J. 23 (1973) 298-305.
9. M. Fiedler, A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory, Czech Math. J. 25 (1975) 619-633.
10. R. Grone, R. Merris, V.S. Sunder, The Laplacian spectrum of a graph, SIAM J. Matrix Anal. Appl. 11 (1990) 218-238.
11. R. Grone, G. Zimmermann, Large eigenvalues of the Laplacian, Linear and Multilinear Algebra 28 (1990) 45-47.
12. P.L. Hammer, A.K. Kelmans, Laplacian spectra and spanning trees of threshold graphs, Discrete Appl. Math. 65 (1996) 255-273.
13. B.D. McKay, On the spectral characteristics of trees, Ars Combin. 3 (1977) 219-232.
14. R. Merris, Degree maximal graphs are Laplacian integral, Linear Algebra Appl. 199 (1994) 381-389.
15. R. Merris, Threshold graphs, in: Proceedings of the Prague Mathematical Conference 1996, ICARIS Ltd., Prague, pp. 205-210.
16. R. Merris, Multilinear Algebra, Gordon and Breach, Amsterdam, 1997.
17. R. Merris, Large families of Laplacian isospectral graphs, Linear and Multilinear Algebra 43 (1997) 201-205.
18. J.W. Moon, L. Moser, Almost all (0,1)-matrices are primitive, Studia Math. Hungar. 1 (1996) 153-156.
19. A.J. Schwenk, Exactly thirteen connected cubic graphs have integral spectra, in: Y. Alavi, D.R. Lieh (Eds.), Theory and Applications of Graphs, Lecture Notes in Math., vol. 642, Springer, Berlin, 1978, pp. 516-533.
20. D.B. West, Introduction to Graph Theory, Prentice-Hall, Upper Saddle River, NJ, 1996.
21. E.S. Wolk, A note on the comparability graph of a tree, Proc. Am. Math. Soc. 16 (1965) 17-20.