SPEKTRALNO PREPOZNAVANJE GRAFOVA I MREŽA

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SPEKTRALNO PREPOZNAVANJE GRAFOVA I MREŽA

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dc.contributor.advisor Stanić, Zoran
dc.contributor.author Jovanović, Irena
dc.date.accessioned 2016-06-24T14:29:40Z
dc.date.available 2016-06-24T14:29:40Z
dc.date.issued 2014
dc.identifier.uri http://hdl.handle.net/123456789/4233
dc.description.abstract Spectral graph theory is a mathematical theory where graphs are considered by means of the eigenvalues and the corresponding eigenvectors of the matrices that are assigned to them. The spectral recognition problems are of particular interest. Between them we can distinguish: characterizations of graphs with a given spectrum, exact or approximate constructions of graphs with a given spectrum, similarity of graphs and perturbations of graphs. In this dissertation we are primarily interested for the similarity of graphs, where graphs with the same number of vertices and graphs of different orders are considered. Similarity of graphs of equal orders can be established by computation of the spectral distances between them, while for graphs with different number of vertices the measures of similarity are introduced. In that case, graphs under study are usually very large and they are denoted as networks, while the measures of similarity can be spectraly based. Some mathematical results on the Manhattan spectral distance of graphs based on the adjacency matrix, Laplacian and signless Laplacian matrix are given in this dissertation. A new measure of similarity for the vertices of the networks under study is proposed. It is based on the difference of the generating functions for the numbers of closed walks in the vertices of networks. These closed walks are calculated according to the new spectral formula which enumerates the numbers of spanning closed walks in the graphlets of the corresponding graphs. The problem of the characterization of a digraph with respect to the spectrum of AAT , apropos ATA, where A is the adjacency matrix of a digraph, is introduced. The notion of cospectrality is generalized, and so the cospectrality between some particular digraphs with respect to the matrix AAT and multigraphs with respect to the signless Laplacian matrix is considered. en_US
dc.description.provenance Submitted by Slavisha Milisavljevic (slavisha) on 2016-06-24T14:29:40Z No. of bitstreams: 1 Jovanović_Irena.pdf: 1138369 bytes, checksum: 4a1a7f55f6c3524b240426ad818b9158 (MD5) en
dc.description.provenance Made available in DSpace on 2016-06-24T14:29:40Z (GMT). No. of bitstreams: 1 Jovanović_Irena.pdf: 1138369 bytes, checksum: 4a1a7f55f6c3524b240426ad818b9158 (MD5) Previous issue date: 2014 en
dc.language.iso sr en_US
dc.publisher Beograd en_US
dc.title SPEKTRALNO PREPOZNAVANJE GRAFOVA I MREŽA en_US
mf.author.birth-date 1981
mf.author.birth-place Kragujevac en_US
mf.author.birth-country Srbija en_US
mf.author.residence-state Srbija en_US
mf.author.citizenship Srpsko en_US
mf.author.nationality Srpkinja en_US
mf.subject.keywords graph, digraph, spectrum, spectral distance, closed walk, spanning closed walk, graphlet, cospectrality, generating function en_US
mf.contributor.committee Stanić, Zoran
mf.contributor.committee Cvetković, Dragoš
mf.contributor.committee Jovanović, Boško
mf.university.faculty Mathematical Faculty en_US
mf.document.references 95 en_US
mf.document.pages 155 en_US
mf.document.location Beograd en_US
mf.document.genealogy-project No en_US
mf.university Belgrade University en_US

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