Geodesic
TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, I
Publications de l'Institut Mathématique, _N_S_85 (2009) no. 99, p. 19 .

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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 ađacency 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.
DOI : 10.2298/PIM0999019C
Classification : 05C50
Keywords: graph theory, graph spectra, ađacency matrix, signless Laplacian 
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Dragoš Cvetković; Slobodan K. Simić. TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, I. Publications de l'Institut Mathématique, _N_S_85 (2009) no. 99, p. 19 . doi : 10.2298/PIM0999019C. http://geodesic.mathdoc.fr/articles/10.2298/PIM0999019C/

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