|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||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 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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