Let A_G and D_G be respectively the adjacency matrix and the degree matrix of a graph G. The signless Laplacian matrix of G is defined as Q_G=D_G+A_G. The Q-spectrum of G is the set of the eigenvalues together with their multiplicities of QG. The Q-index of G is the maximum eigenvalue of Q_G. The possibilities for developing a spectral theory of graphs based on the signless Laplacian matrices were discussed by Cvetković et al. [D. Cvetković, P. Rowlinson, S.K. Simić, Signless Laplacians of finite graphs, Linear Algebra Appl. 423 (2007) 155–171]. In the latter paper the authors determine the graphs whose Q-index is in the interval [0,4]. In this paper, we investigate some properties of Q-spectra of graphs, especially for the limit points of the Q-index. By using these results, we characterize respectively the structures of graphs whose the Q-index lies in the intervals (4,2+sqrt 5), (2+sqrt 5,ϵ+2) and (ϵ+2,4.5], where ϵ=1/3((54-6 sqrt 33)^1/3+(54+ 6 sqrt 33)^1/3)\approx 2.382975767. © 2009 Elsevier Inc. All rights reserved.

On graphs whose signless Laplacian index does not exceed 4.5

BELARDO, FRANCESCO;LI MARZI, Enzo
2009

Abstract

Let A_G and D_G be respectively the adjacency matrix and the degree matrix of a graph G. The signless Laplacian matrix of G is defined as Q_G=D_G+A_G. The Q-spectrum of G is the set of the eigenvalues together with their multiplicities of QG. The Q-index of G is the maximum eigenvalue of Q_G. The possibilities for developing a spectral theory of graphs based on the signless Laplacian matrices were discussed by Cvetković et al. [D. Cvetković, P. Rowlinson, S.K. Simić, Signless Laplacians of finite graphs, Linear Algebra Appl. 423 (2007) 155–171]. In the latter paper the authors determine the graphs whose Q-index is in the interval [0,4]. In this paper, we investigate some properties of Q-spectra of graphs, especially for the limit points of the Q-index. By using these results, we characterize respectively the structures of graphs whose the Q-index lies in the intervals (4,2+sqrt 5), (2+sqrt 5,ϵ+2) and (ϵ+2,4.5], where ϵ=1/3((54-6 sqrt 33)^1/3+(54+ 6 sqrt 33)^1/3)\approx 2.382975767. © 2009 Elsevier Inc. All rights reserved.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11570/16280
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 34
  • ???jsp.display-item.citation.isi??? 32
social impact