Authors: Andelić, Milica
Da Fonseca, Carlos
Simić, Slobodan 
Tošić, Dejan
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Connected graphs of fixed order and size with maximal Q-index: Some spectral bounds
Journal: Discrete Applied Mathematics
Volume: 160
Issue: 4-5
First page: 448
Last page: 459
Issue Date: 1-Mar-2012
Rank: M22
ISSN: 0166-218X
DOI: 10.1016/j.dam.2011.11.001
The Q-index of a simple graph G is the largest eigenvalue of the matrix Q, the signless Laplacian of G. It is well-known that in the set of connected graphs with fixed order and size, the graphs with maximal Q-index are the nested split graphs (also known as threshold graphs). In this paper, we focus our attention on the eigenvector techniques for getting some (lower and upper) bounds on the Q-index of nested split graphs. In addition, we give some computational results in order to compare these bounds.
Keywords: Largest eigenvalue | Nested split graph | Signless Laplacian | Spectral bounds | Spectral radius | Threshold graph
Publisher: Elsevier
Project: Graph theory and mathematical programming with applications in chemistry and computer science 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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