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Signless Laplacians of finite graphs

Cvetkovic D, Rowlinson P & Simic SK (2007) Signless Laplacians of finite graphs. Linear Algebra and Its Applications, 423 (1), pp. 155-171.

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.

Graph theory; Graph spectra; Line graph; Signless Laplacian; Star complement

Linear Algebra and Its Applications: Volume 423, Issue 1

Author(s)Cvetkovic, Dragos; Rowlinson, Peter; Simic, Slobodan K
Publication date31/05/2007
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