Authors: Cvetković, Dragoš
Simić, Slobodan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Towards a spectral theory of graphs based on the signless Laplacian, II
Journal: Linear Algebra and Its Applications
Volume: 432
Issue: 9
First page: 2257
Last page: 2272
Issue Date: 15-Apr-2010
Rank: M22
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.05.020
Abstract: 
A spectral graph theory is a theory in which graphs are studied by means of eigenvalues of a matrix M which is in a prescribed way defined for any graph. This theory is called M-theory. We outline a spectral theory of graphs based on the signless Laplacians Q and compare it with other spectral theories, in particular to those based on the adjacency matrix A and the Laplacian L. As demonstrated in the first part, the Q-theory can be constructed in part using various connections to other theories: equivalency with A-theory and L-theory for regular graphs, common features with L-theory for bipartite graphs, general analogies with A-theory and analogies with A-theory via line graphs and subdivision graphs. In this part, we introduce notions of enriched and restricted spectral theories and present results on integral graphs, enumeration of spanning trees, characterizations by eigenvalues, cospectral graphs and graph angles.
Keywords: Adjacency matrix | Graph spectra | Graph theory | Laplacian | Signless Laplacian
Publisher: Elsevier
Project: Serbian Ministry of Science and Technological Development, Grant 144015G

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