Cospectrality of multipartite graphs - Abdollahi, Alireza (Ars mathematica contemporanea, 2022)
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 cospectralities of the cocktail party graph and the complete tripartite graph with parts of the same size to the Euclidean or Manhattan norms.
Keywords: adjacency matrix of a graph; cospectrality of graphs; Euclidean norm; evklidska norma; kospektralnost grafov; Manhattan norm; manhattanska norma; matrika sosednosti grafa; spectra of graphs; spektri grafov