# SPEKTRALNO PREPOZNAVANJE GRAFOVA I MREŽA

 Title: SPEKTRALNO PREPOZNAVANJE GRAFOVA I MREŽA Author: Jovanović, Irena 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. URI: http://hdl.handle.net/123456789/4233 Date: 2014

## Files in this item

Files Size Format View
Jovanović_Irena.pdf 1.138Mb PDF View/Open

The following license files are associated with this item: