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
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 

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