Open AccessCospectrality graphs of Smith graphs
Author(s) -
M Dragos Cvetkovic,
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 , pathwidth , discrete mathematics , modular decomposition , 1 planar graph , algebraic graph theory , algebraic properties , 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.