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Title: Main eigenvalues and (κ, τ)-regular sets
Author: Cardoso, Domingos M.
Sciriha, I.
Zerafa, C.
Keywords: (κ, τ)-Regular sets
Main eigenspaces
Main eigenvalues
Adjacency matrices
Regular sets
Spectral radii
Strongly regular graphs
Issue Date: 2010
Publisher: Elsevier
Abstract: A (κ, τ)-regular set is a subset of the vertices of a graph G, inducing a κ-regular subgraph such that every vertex not in the subset has τ neighbors in it. A main eigenvalue of the adjacency matrix A of a graph G has an eigenvector not orthogonal to the all-one vector j. For graphs with a (κ, τ)-regular set a necessary and sufficient condition for an eigenvalue be non-main is deduced and the main eigenvalues are characterized. These results are applied to the construction of infinite families of bidegreed graphs with two main eigenvalues and the same spectral radius (index) and some relations with strongly regular graphs are obtained. Finally, the determination of (κ, τ)-regular sets is analyzed. © 2009 Elsevier Inc. All rights reserved.
Peer review: yes
ISSN: 0024-3795
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Appears in Collections:DMat - Artigos

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