The spectra of undirected de Bruijn graphs and an upper bound for their independence numbers

Abstract

Using the unitary similarity transformation of the adjacency matrix, we obtain a new upper bound for the independence number of the de Bruijn graph based on the spectrum of the undirected de Bruijn graph. In the case of a <?-ary graph of degree n this bound is of the form 7Γ 2 \ a" 1~' where &, -> 0 as n -> «>.