A lower bound for the Laplacian eigenvalues of a graph—Proof of a conjecture by Guo

By A. E. Brouwer, Willem H. Haemers. 2008

53 citations recorded by the source corpus.

We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j n) of a connected graph 蚠 on n vertices, then μj dj − j + 2 (1 j n − 1). This settles a conjecture due to Guo.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/f10ae559b9ff043ef0492df8f15722b3d16a1bd8

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In Discrete Mathematics and Combinatorics

1. Andries E. Brouwer
2. Willem H. Haemers

In Geometry and Topology

1. Andries E. Brouwer
2. Ali Mohammadian
3. Willem H. Haemers
4. Sebastian M. Cioaba
5. Dragos M. Cvetkovic
6. David A. Gregory
7. Slobodan K. Simic

In Organic Chemistry

1. Willem H. Haemers
2. Andries E. Brouwer

Citations in the corpus

• On the sum of Laplacian eigenvalues of graphs (2010, background): “Theorem 3 [ 1 ] Let G be a graph with n vertices and vertex degrees d1 > � � � > dn. If G is not Ks + (n − s)K1, then � s(G) > ds − s + 2 for 1 6 s 6 n.”
• Spectra of Graphs (2011, background): “51 3.7.2 The Haemers bound on the Shannon capacity . . . . . .”