TY: JOUR T1 - On the Laplacian and signless Laplacian spectrum of a graph with k pairwise co-neighbor vertices A1 - Abreu, Nair M.M. A1 - Cardoso, Domingos Moreira A1 - Martins, Enide A. A1 - Robbiano, Maria A1 - San Martin, B. N2 - 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 + ? for each nonzero Laplacian eigenvalue ? of Gk. The Laplacian spectrum of G overlaps the Laplacian spectrum of Gk in at least n ? k + 1 places. UR - https://ria.ua.pt/handle/10773/13101 Y1 - 2012 PB - Elsevier