Authors: Simić, Slobodan 
Belardo, Francesco
Li Marzi, Enzo Maria
Tošić, Dejan
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Connected graphs of fixed order and size with maximal index: Some spectral bounds
Journal: Linear Algebra and Its Applications
Volume: 432
Issue: 9
First page: 2361
Last page: 2372
Issue Date: 15-Apr-2010
Rank: M22
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.06.043
The index (or spectral radius) of a simple graph is the largest eigenvalue of its adjacency matrix. For connected graphs of fixed order and size the graphs with maximal index are not yet identified (in the general case). It is known (for a long time) that these graphs are nested split graphs (or threshold graphs). In this paper we use the eigenvector techniques for getting some new (lower and upper) bounds on the index of nested split graphs. Besides we give some computational results in order to compare these bounds.
Keywords: Adjacency spectrum | Graph index | Largest eigenvalue | Nested split graph | Spectral bounds | Spectral radius | Threshold graph
Publisher: Elsevier
Project: Serbian Ministry of Science, Grants 144015G and TR-11021
MIUR (cofin “Strutture geometriche, combinatorie e loro applicazioni")

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