Main eigenvalues and (κ, τ)-regular sets
Data(s) |
31/10/2011
2010
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Resumo |
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. CEOC FCT FEDER/POCI 2010 University of Malta |
Identificador |
0024-3795 |
Idioma(s) |
eng |
Publicador |
Elsevier |
Relação |
http://www.scopus.com/inward/record.url?eid=2-s2.0-77049101695&partnerID=40&md5=e55dce8d7dbe46613e682a054a70b694 http://www.sciencedirect.com/science/article/pii/S002437950900442X |
Direitos |
restrictedAccess restrictedAccess |
Palavras-Chave | #(κ, τ)-Regular sets #Main eigenspaces #Main eigenvalues #Adjacency matrices #Regular sets #Spectral radii #Strongly regular graphs |
Tipo |
article |