Authors: Cvetković, Dragoš
Rowlinson, Peter
Simić, Slobodan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Signless Laplacians of finite graphs
Journal: Linear Algebra and Its Applications
Volume: 423
Issue: 1
First page: 155
Last page: 171
Issue Date: 1-May-2007
Rank: M22
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.01.009
Abstract: 
We survey properties of spectra of signless Laplacians of graphs and discuss possibilities for developing a spectral theory of graphs based on this matrix. For regular graphs the whole existing theory of spectra of the adjacency matrix and of the Laplacian matrix transfers directly to the signless Laplacian, and so we consider arbitrary graphs with special emphasis on the non-regular case. The results which we survey (old and new) are of two types: (a) results obtained by applying to the signless Laplacian the same reasoning as for corresponding results concerning the adjacency matrix, (b) results obtained indirectly via line graphs. Among other things, we present eigenvalue bounds for several graph invariants, an interpretation of the coefficients of the characteristic polynomial, a theorem on powers of the signless Laplacian and some remarks on star complements.
Keywords: Graph spectra | Graph theory | Line graph | Signless Laplacian | Star complement
Publisher: Elsevier
Project: EPSRC, grant EP/D010748/1
Serbian Ministry of Science and Environmental Protection, Grant 144015G

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