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 |
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 |
URI: | http://hdl.handle.net/10773/4298 |
ISSN: | 0012-365X |
Publisher Version: | http://www.sciencedirect.com/science/article/pii/S0012365X06007254 |
Appears in Collections: | DMat - Artigos |
Files in This Item:
File | Description | Size | Format | |
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CardosoRama2007.pdf | Versão Electrónica | 223.58 kB | Adobe PDF |
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