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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Grone-Merris Conjecture


Author: Hua Bai
Journal: Trans. Amer. Math. Soc. 363 (2011), 4463-4474
MSC (2010): Primary 15A42; Secondary 05C50
Published electronically: March 23, 2011
MathSciNet review: 2792996
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Abstract: In spectral graph theory, the Grone-Merris Conjecture asserts that the spectrum of the Laplacian matrix of a finite graph is majorized by the conjugate degree sequence of this graph. We give a complete proof for this conjecture.


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Additional Information

Hua Bai
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
Email: baihu@bc.edu, huabai@alumni.usc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05393-6
PII: S 0002-9947(2011)05393-6
Keywords: Grone-Merris Conjecture, Laplacian matrix, majorization, split graph, Courant-Fischer-Weyl Min-Max Principle, simplicial complex
Received by editor(s): November 12, 2009
Received by editor(s) in revised form: December 11, 2009, January 1, 2010, and May 28, 2010
Published electronically: March 23, 2011
Additional Notes: The author was partially supported by NSF grant DMS-0604866
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.