Publications de l'Institut Mathématique, Nouvelle Série Vol. 85(99), pp. 19–33 (2009) 

TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, IDragos Cvetkovic and Slobodan K. SimicMatematicki institut SANU, Kneza Mihaila 36, 11000 Beograd, p.p. 367, SerbiaAbstract: 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 $M$\emph{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: graph theory; graph spectra; adjacency matrix; signless Laplacian Classification (MSC2000): 05C50 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 23 Apr 2009. This page was last modified: 22 Oct 2009.
© 2009 Mathematical Institute of the Serbian Academy of Science and Arts
