Cospectrality of graphs.

Abstract: Richard Brualdi proposed in Stevanivić (2007) [6] the following problem: (Problem AWGS.4) Let and be two nonisomorphic graphs on n vertices with spectra respectively. Define the distance between the spectra of and as Define the cospectrality of by Let In this paper we study Problem A and determine the cospectrality of certain graphs by the Euclidian distance. Let denote the complete graph on n vertices, denote the null graph on n vertices and denote the disjoint union of the with isolated vertices, where . In this paper we find , , ( ) and . [Copyright &y& Elsevier]