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Title: On the Laplacian and signless Laplacian spectrum of a graph with k pairwise co-neighbor vertices
Author: Abreu, Nair M.M.
Cardoso, Domingos Moreira
Martins, Enide A.
Robbiano, Maria
San Martin, B.
Keywords: Graph eigenvalues
Signless Laplacian spectrum
Laplacian Spectrum
Pairwise co-neighbor vertices
Issue Date: Nov-2012
Publisher: Elsevier
Abstract: Consider the Laplacian and signless Laplacian spectrum of a graph G of order n, with k pairwise co-neighbor vertices. We prove that the number of shared neighbors is a Laplacian and a signless Laplacian eigenvalue of G with multiplicity at least k− 1. Additionally, considering a connected graph Gk with a vertex set defined by the k pairwise co-neighbor vertices of G, the Laplacian spectrum of Gk, obtained from G adding the edges of Gk, includes l + β for each nonzero Laplacian eigenvalue β of Gk. The Laplacian spectrum of G overlaps the Laplacian spectrum of Gk in at least n − k + 1 places.
Peer review: yes
DOI: 10.1016/j.laa.2012.05.013
ISSN: 0024-3795
Appears in Collections:CIDMA - Artigos

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