THE GRONE-MERRIS CONJECTURE

@inproceedings{Bai2011THEGC,
  title={THE GRONE-MERRIS CONJECTURE},
  author={Hua Bai},
  year={2011}
}
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. The Laplacian of a simple graph G with n vertices is a positive semi-definite n×n matrix L(G) that mimics the geometric Laplacian of a Riemannian manifold; see §1 for definitions, and [2, 14] for comprehensive bibliographies on the graph Laplacian. The spectrum sequence… CONTINUE READING

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