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http://hdl.handle.net/10773/16521
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DC Field | Value | Language |
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dc.contributor.author | Cardoso, Domingos M. | pt |
dc.contributor.author | Rojo, Oscar | pt |
dc.date.accessioned | 2016-12-15T11:28:24Z | - |
dc.date.issued | 2017-01 | - |
dc.identifier.issn | 0024-3795 | pt |
dc.identifier.uri | http://hdl.handle.net/10773/16521 | - |
dc.description.abstract | Let G be a simple undirected graph of order n. A cluster in G of order c and degree s, is a pair of vertex subsets (C, S), where C is a set of cardinality |C| =c ≥2 of pairwise co-neighbor vertices sharing the same set S of s neighbors. Assuming that the graph G has k≥1 clusters (C_1, S_1), ..., (C_k, S_k), consider a family of k graphs H_1, ..., H_k and the graph G(H_1, ..., H_k) which is obtained from G after adding the edges of the graphs H_1, ..., H_ k whose vertex set of each H_j is identified with C_j, for j=1, ..., k. The Laplacian eigenvalues of G(H_1, ..., H_k)remain the same, independently of the graphs H_1, ..., H_k, with the exception of |C_1| +···+|C_k| −k of them. These new Laplacian eigenvalues are determined using a unified approach which can also be applied to the determination of a same number of adjacency and signless Laplacian eigenvalues when the graphs H_1, ..., H_k are regular. The Faria’s lower bound on the multiplicity of the Laplacian eigenvalue 1 of a graph with pendant vertices is generalized. Furthermore, the algebraic connectivity and the Laplacian index of G(H_1, ..., H_k) remain the same, independently of the graphs H_1, ..., H_k. | pt |
dc.language.iso | eng | pt |
dc.publisher | Elsevier | pt |
dc.relation | UID/MAT/04106/2013 | pt |
dc.relation | FONDECYTRegular 1130135 | pt |
dc.rights | restrictedAccess | por |
dc.subject | Adjacency, Laplacian and signless Laplacian spectra of graphs | pt |
dc.subject | Graph cluste | pt |
dc.subject | Algebraic connectivity | pt |
dc.subject | Laplacian index | pt |
dc.subject | Adjacency index | pt |
dc.title | Edge perturbation on graphs with clusters: Adjacency, Laplacian and signless Laplacian eigenvalues | pt |
dc.type | article | pt |
dc.peerreviewed | yes | pt |
ua.distribution | international | pt |
degois.publication.firstPage | 113 | pt |
degois.publication.lastPage | 128 | pt |
degois.publication.title | Linear Algebra and its Applications | pt |
degois.publication.volume | 512 | pt |
dc.date.embargo | 10000-01-01 | - |
dc.identifier.doi | 10.1016/j.laa.2016.09.031 | pt |
Appears in Collections: | CIDMA - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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1-s2.0-S002437951630430X-main.pdf | 327.2 kB | Adobe PDF |
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