Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/16230
Title: | Extremal graphs for the sum of the two largest signless Laplacian eigenvalues |
Author: | Oliveira, Carla Silva Lima, Leonado de Rama, Paula Carvalho, Paula |
Keywords: | Signless Laplacian Sum of eigenvalues Extremal graphs |
Issue Date: | Oct-2015 |
Publisher: | ILAS–the International Linear Algebra Society (ILAS) |
Abstract: | Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A, where A is the adjacency matrix and D is the diagonal matrix of the vertices degree of G. Let q1(G) and q2(G) be the first and the second largest eigenvalues of Q(G), respectively, and denote by S+ n the star graph with an additional edge. It is proved that inequality q1(G)+q2(G) e(G)+3 is tighter for the graph S+ n among all firefly graphs and also tighter to S+ n than to the graphs Kk _ Kn−k recently presented by Ashraf, Omidi and Tayfeh-Rezaie. Also, it is conjectured that S+ n minimizes f(G) = e(G) − q1(G) − q2(G) among all graphs G on n vertices. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/16230 |
DOI: | 10.13001/1081-3810.3143 |
ISSN: | 1081-3810 |
Appears in Collections: | CIDMA - Artigos OGTCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Extremal graphs for signless Laplacian eigenvalues(1).pdf | Documento principal | 185.35 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.