Characterizing identifying codes from the spectrum of a graph or digraph

Abstract

A -identifying code in digraph D is a dominating subset C of vertices of D, such that all distinct subsets of vertices of D with cardinality at most l have distinct closed in-neighborhoods within C. As far as we know, it is the very first time that the spectral graph theory has been applied to the identifying codes. We give a new method to obtain an upper bound on l for digraphs. The results obtained here can also be applied to graphs.