A majorization bound for the eigenvalues of some graph laplacians

SIAM Journal on Discrete Mathematics

Volumn 21, Issue 2, 2007, Pages 303-312

  Stephen, Tamon ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Degree sequence; Dirichlet Laplacian; Graph laplacian; Graph spectrum; Majorization

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; GRAPH THEORY;

(R ,S)-CONJUGATE; APPLIED MATHEMATICS; DIRICHLET BOUNDARY CONDITIONS; EIGENVALUES (OF GRAPHS); GRAPH LAPLACIANS; LAPLACIAN SPECTRUM; MAJORIZATION; OF GRAPHS; VERTEX DEGREES;

TREES (MATHEMATICS);

EID: 45249110216     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/040619594     Document Type: Article

References (10)

1. F. R. K. CHUNG AND R. B. ELLIS, A chip-firing game and Dirichlet eigenvalues, Discrete Math., 257 (2002), pp. 341-355.
2. F. R. K. CHUNG AND R. P. LANGLANDS, A combinatorial Laplacian with vertex weights, J. Combin. Theory Ser. A, 75 (1996), pp. 316-327.
3. A. M. DUVAL, A common recursion for Laplacians of matroids and shifted simplicial complexes, Doc. Math., 10 (2005), pp. 583-618.
4. A. M. DUVAL AND V. REINER, Shifted simplicial complexes are Laplacian integral, Trans. Amer. Math. Soc., 354 (2002), pp. 4313-4344.
5. R. GRONE AND R. MERRIS, The Laplacian spectrum of a graph II, SIAM J. Discrete Math., 7 (1994), pp. 221-229.
6. P. L. HAMMER AND A. K. KELMANS, Laplacian spectra and spanning trees of threshold graphs, Discrete Appl. Math., 65 (1996), pp. 255-273.
7. R. A. HORN AND C. R. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1990. Corrected reprint of the 1985 original.
8. N. V. R. MAHADEV AND U. N. PELED, Threshold Graphs and Related Topics, Ann. Discrete Math. 56, North-Holland, Amsterdam, 1995.
9. A. W. MARSHALL AND I. OLKIN, Inequalities: Theory of Majorization and Its Applications, Math. Sci. Engrg. 143, Academic Press, New York, 1979.
10. J. R. MUNKRES, Elements of Algebraic Topology, Addison-Wesley, Menlo Park, CA, 1984.