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http://hdl.handle.net/1893/18460| Appears in Collections: | Computing Science and Mathematics Journal Articles |
| Peer Review Status: | Refereed |
| Title: | Signless Laplacians of finite graphs |
| Author(s): | Cvetkovic, Dragos Rowlinson, Peter Simic, Slobodan K |
| Contact Email: | peter.rowlinson@stir.ac.uk |
| Keywords: | Graph theory Graph spectra Line graph Signless Laplacian Star complement |
| Issue Date: | May-2007 |
| Date Deposited: | 28-Jan-2014 |
| Citation: | Cvetkovic D, Rowlinson P & Simic SK (2007) Signless Laplacians of finite graphs. Linear Algebra and Its Applications, 423 (1), pp. 155-171. https://doi.org/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. |
| DOI Link: | 10.1016/j.laa.2007.01.009 |
| Rights: | Made available under an Elsevier Open Archive user license: Articles published under an Elsevier user license are protected by copyright and may be used for non-commercial purposes. Users may access, download, copy, display, redistribute, adapt, translate, text mine and data mine the articles provided that users: •Cite the article using an appropriate bibliographic citation (i.e. author(s), journal, article title, volume, issue, page numbers, DOI and the link to the definitive published version on ScienceDirect) •Use the article for non- commercial purposes •Maintain the integrity of the article •Retain copyright notices and links to these terms and conditions so it is clear to other users what can and cannot be done with the article •Ensure that, for any content in the article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party This is a non commercial license where the use of published articles for commercial purposes is prohibited. |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| Signless Laplacians Open Archive.pdf | Fulltext - Published Version | 190.7 kB | Adobe PDF | View/Open |
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