In this paper, we consider the signless Laplacians of simple graphs and we give some eigenvalue inequalities. We first consider an interlacing theorem when a vertex is deleted. In particular, let G-v be a graph obtained from graph G by deleting its vertex v and κi(G) be the ith largest eigenvalue of the signless Laplacian of G , we show that κi+1(G)-1⩽κi(G-v)⩽κi(G). Next, we consider the third largest eigenvalue κ3(G) and we give a lower bound in terms of the third largest degree d3 of the graph G . In particular, we prove that κ3(G)≥d3(G)-2.. Furthermore, we show that in several situations the latter bound can be increased to d3-1.

A note on the signless laplacian eigenvalues of graphs

Abstract

In this paper, we consider the signless Laplacians of simple graphs and we give some eigenvalue inequalities. We first consider an interlacing theorem when a vertex is deleted. In particular, let G-v be a graph obtained from graph G by deleting its vertex v and κi(G) be the ith largest eigenvalue of the signless Laplacian of G , we show that κi+1(G)-1⩽κi(G-v)⩽κi(G). Next, we consider the third largest eigenvalue κ3(G) and we give a lower bound in terms of the third largest degree d3 of the graph G . In particular, we prove that κ3(G)≥d3(G)-2.. Furthermore, we show that in several situations the latter bound can be increased to d3-1.
Scheda breve Scheda completa Scheda completa (DC)
File in questo prodotto:
File
A note on the signless Laplacian eigenvalues of graphs.pdf

non disponibili

Descrizione: Articolo completo in Post-print
Tipologia: Documento in Post-print
Licenza: Accesso privato/ristretto
Dimensione 187.84 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/11588/618966`