Cospectrality of multipartite graphs

Abstract

Let G be a graph on n vertices and consider the adjacency spectrum of G as the ordered n -tuple whose entries are eigenvalues of G written decreasingly. Let G and H be two non-isomorphic graphs on n vertices with spectra S and T , respectively. Define the distance between the spectra of G and H as the distance of S and T to a norm N of the n -dimensional vector space over real numbers. Define the cospectrality of G as the minimum of distances between the spectrum of G and spectra of all other non-isomorphic n vertices graphs to the norm N . In this paper we investigate copsectralities of the cocktail party graph and the complete tripartite graph with parts of the same size to the Euclidean or Manhattan norms.