Cospectrality graphs of Smith graphs | Zendy

Dragoš Cvetković | Zendy; Vesna Todorčević | Zendy

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Cospectrality graphs of Smith graphs

Author(s) -

Dragoš Cvetković,

Vesna Todorčević

Publication year - 2019

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1911269c

Subject(s) - mathematics , diophantine equation , indifference graph , algebraic number , chordal graph , discrete mathematics , pathwidth , modular decomposition , algebraic properties , 1 planar graph , algebraic graph theory , maximal independent set , combinatorics , graph , line graph , mathematical analysis

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.

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