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 Spectral results on regular graphs with (k, τ)-regular sets
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/4298

title: Spectral results on regular graphs with (k, τ)-regular sets
authors: 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.
URI: http://hdl.handle.net/10773/4298
ISSN: 0012-365X
publisher version/DOI: http://www.sciencedirect.com/science/article/pii/S0012365X06007254
source: Discrete Mathematics
appears in collectionsMAT - Artigos

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