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Title: Spectral results on regular graphs with (k, τ)-regular sets
Author: Cardoso, D.M.
Rama, P.
Keywords: Adjacency matrix
Graph eigenvalues
Eigenvalues and eigenfunctions
Matrix algebra
Spectrum analysis
Adjacency matrix
Combinatorial structure
Seidel switching
Graph theory
Issue Date: 2007
Publisher: Elsevier
Abstract: A set of vertices S icluded in V (G) is (k, τ)-regular if it induces a k-regular subgraph of G such that | NG (v) ∩ S | = τ if v is not in S. Note that a connected graph with more than one edge has a perfect matching if and only if its line graph has a (0, 2)-regular set. In this paper, some spectral results on the adjacency matrix of graphs with (k, τ)-regular sets are presented. Relations between the combinatorial structure of a p-regular graph with a (k, τ)-regular set and the eigenspace corresponding to each eigenvalue λ not in { p, k - τ } are deduced. Finally, additional results on the effects of Seidel switching (with respect to a bipartition induced by S) of regular graphs are also introduced. © 2006 Elsevier B.V. All rights reserved.
Peer review: yes
ISSN: 0012-365X
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Appears in Collections:DMat - Artigos

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