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, I
Journal: Publications de l'Institut Mathematique
Volume: 85
Issue: 99
First page: 19
Last page: 33
Issue Date: 29-Jun-2009
Rank: M24
ISSN: 0350-1302
DOI: 10.2298/PIM0999019C
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 with those based on the adjacency matrix A and the Laplacian L. The Q-theory can be composed using various connections to other theories: equivalency with A-theory and L-theory for regular graphs, or with L-theory for bipartite graphs, general analogies with A-theory and analogies with A-theory via line graphs and subdivision graphs. We present results on graph operations, inequalities for eigenvalues and reconstruction problems.
Keywords: Adjacency matrix | Graph spectra | Graph theory | Signless laplacian
Publisher: Mathematical Institute of the SASA
Project: Serbian Ministry of Science and Technological Development, Grant 144015G

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