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» On the largest eigenvalue of non-regular graphs
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JCT
2007
119views more  JCT 2007»
13 years 7 months ago
Cliques and the spectral radius
We prove a number of relations between the number of cliques of a graph G and the largest eigenvalue (G) of its adjacency matrix. In particular, writing ks (G) for the number of s...
Béla Bollobás, Vladimir Nikiforov
COMBINATORICS
2007
99views more  COMBINATORICS 2007»
13 years 7 months ago
The Spectral Radius of Subgraphs of Regular Graphs
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) Let G be a regular graph of order n and finite di...
Vladimir Nikiforov
COMBINATORICS
2007
100views more  COMBINATORICS 2007»
13 years 7 months ago
Revisiting Two Classical Results on Graph Spectra
Let µ (G) and µmin (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) If H is a proper subgraph of a connected graph G o...
Vladimir Nikiforov
PAKDD
2011
ACM
209views Data Mining» more  PAKDD 2011»
12 years 10 months ago
Spectral Analysis for Billion-Scale Graphs: Discoveries and Implementation
Abstract. Given a graph with billions of nodes and edges, how can we find patterns and anomalies? Are there nodes that participate in too many or too few triangles? Are there clos...
U. Kang, Brendan Meeder, Christos Faloutsos
IPCO
1993
98views Optimization» more  IPCO 1993»
13 years 8 months ago
A spectral approach to bandwidth and separator problems in graphs
Lower bounds on the bandwidth, the size of a vertex separator of general undirected graphs, and the largest common subgraph of two undirected (weighted) graphs are obtained. The b...
Christoph Helmberg, Bojan Mohar, Svatopluk Poljak,...