Authors: | Cvetković, Dragoš Todorčević, Vesna |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Cospectrality graphs of smith graphs | Journal: | Filomat | Volume: | 33 | Issue: | 11 | First page: | 3269 | Last page: | 3276 | Issue Date: | 1-Jan-2019 | Rank: | M22 | ISSN: | 0354-5180 | DOI: | 10.2298/FIL1911269C | URL: | http://www.doiserbia.nb.rs/img/doi/0354-5180/2019/0354-51801911269C.pdf | Abstract: | Graphs whose spectrum belongs to the interval [−2, 2] are called Smith graphs. The structure of a Smith graph with a given spectrum depends on a system of Diophantine linear algebraic equations. We have established in [1] several properties of this system and showed how it can be simplified and effectively applied. In this way a spectral theory of Smith graphs has been outlined. In the present paper we introduce cospectrality graphs for Smith graphs and study their properties through examples and theoretical consideration. The new notion is used in proving theorems on cospectrality of Smith graphs. In this way one can avoid the use of the mentioned system of Diophantine linear algebraic equations. |
Keywords: | Cospectrality graphs | Diophantine equations | Smith graphs | Spectral graph theory | Spectral radius | Publisher: | Faculty of Sciences and Mathematics, University of Niš | Project: | Graph theory and mathematical programming with applications in chemistry and computer science Methods of Functional and Harmonic Analysis and PDE with Singularities F-159 |
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