417 KB34 KB200820252022Abdollahi, AlirezaZakeri, Niloufarštevilka:1letnik:22P1.06 (15 str.)DOI:10.26493/1855-3974.2332.749COBISSID_HOST:115583747ISSN:1855-3966URN:URN:NBN:SI:doc-8UMCT4EUenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaadjacency matrix of a graphcospectrality of graphsEuclidean normevklidska normakospektralnost grafovManhattan normmanhattanska normamatrika sosednosti grafaspectra of graphsspektri grafovCospectrality of multipartite graphs|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 normsNaj bo ?$G$? graf na ?$n$? vozliščih; obravnavajmo spekter sosednosti grafa ?$G$? kot urejeno ?$n$?-terko, katere elementi so lastne vrednosti grafa ?$G$?, zapisane v padajočem vrstnem redu. Naj bosta ?$G$? in ?$H$? dva neizomorfna grafa na ?$n$? vozliščih s spektroma ?$S$? oz. ?$T$?. Definirajmo razdaljo med spektroma grafov ?$G$? in ?$H$? kot razdaljo spektrov ?$S$? in ?$T$? glede na normo ?$N$? ?$n$?-dimenzionalnega vektorskega prostora nad obsegom realnih števil. Definirajmo kospektralnost grafa ?$G$? kot najmanjšo vrednost razdalj med spektrom grafa ?$G$? in spektri vseh drugih temu grafu neizomorfnih ?$n$? vozliščnih grafov glede na normo ?$N$?. V tem raziskujemo kospektralnost cp-grafa ter polnega tridelnega grafa z deli iste velikosti glede na evklidsko in manhattansko normoTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije