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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.
San Martin, B.
Signless Laplacian spectrum
Pairwise co-neighbor vertices
|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.|
|Appears in Collections:||CIDMA - Artigos|
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|on the Laplacian and signless Laplacian.pdf||Documento Principal||338.71 kB||Adobe PDF|
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