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» Eigenvalues of the derangement graph
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EJC
2007
13 years 7 months ago
Nonsingular mixed graphs with few eigenvalues greater than two
Let G be a nonsingular connected mixed graph. We determine the mixed graphs G on at least seven vertices with exactly two Laplacian eigenvalues greater than 2. In addition, all mi...
Yi-Zheng Fan, Shi-Cai Gong, Jun Zhou, Ying-Ying Ta...
FOCS
2009
IEEE
14 years 2 months ago
Higher Eigenvalues of Graphs
— We present a general method for proving upper bounds on the eigenvalues of the graph Laplacian. In particular, we show that for any positive integer k, the kth smallest eigenva...
Jonathan A. Kelner, James R. Lee, Gregory N. Price...
CAI
2007
Springer
14 years 1 months ago
The Second Eigenvalue of Random Walks On Symmetric Random Intersection Graphs
Abstract. In this paper we examine spectral properties of random intersection graphs when the number of vertices is equal to the number of labels. We call this class symmetric rand...
Sotiris E. Nikoletseas, Christoforos Raptopoulos, ...
CORR
2004
Springer
83views Education» more  CORR 2004»
13 years 7 months ago
A proof of Alon's second eigenvalue conjecture and related problems
A d-regular graph has largest or first (adjacency matrix) eigenvalue 1 = d. Consider for an even d 4, a random d-regular graph model formed from d/2 uniform, independent permutat...
Joel Friedman
JCT
2007
83views more  JCT 2007»
13 years 7 months ago
On the largest eigenvalue of non-regular graphs
We study the spectral radius of connected non-regular graphs. Let λ1(n,Δ) be the maximum spectral radius among all connected non-regular graphs with n vertices and maximum degre...
Bolian Liu, Jian Shen, Xinmao Wang