COSPECTRALITY GRAPHS OF SMITH GRAPHS

Abstract

ct. Graphs whose spectrum belongs to the interval [−2,2] are called Smith The structure
of a Smith graph with a given spectrum depends on a system of Diofantine 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 Diofantine linear algebraic
equations.