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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
DOI: 10.13001/1081-3810.3143
ISSN: 1081-3810
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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