2023 128 listova 1513732 bytes Neki doprinosi spektralnoj teoriji grafova https://phaidrani.ni.ac.rs/o:2616 cobiss:138833929 thesis:8704 Damnjanović, Ivan G., 1996- The doctoral dissertation deals with solving three concrete scientificproblems from the field of spectral graph theory. Firstof all, let a nut graph represent a nontrivial simple graph whoseadjacency matrix has a one dimensional null space all of whosenonzero members contain no zero elements. The first resolvedscientific problem is the circulant nut graph existence problemwhich is connected to determining all the pairs (n, d), n EN, d E N0 for which there exists a d-regular circulant nut graphof order n. Furthermore, let a balanced tree be a rooted tree allof whose vertices from the same level have an equal number ofchildren. Also, for any d, k E N, d > 2, let the Bethe tree Bd, krepresent a balanced tree with k levels such that all of its verticesoutside the last level have exactly d - 1 children, and letthe dendrimer Dd, k be a balanced tree with k levels such thatall of its vertices outside the last level are of degree d. The secondscientific problem that the dissertation deals with is thespectral analysis of balanced trees with a special focus on computingthe energy of Bethe trees and approximating the energyof dendrimers. Finally, the goal of the third part of the doctoraldissertation is to determine the energy of the newly introducedmartini graphs for the purpose of disproving a conjecture previouslydisclosed by Akbari et al. Biografija autora: list 128Bibliografija: listovi 114-119 Datum odbrane: 1.7.2024. Graph Theory info:eu-repo/semantics/bachelorThesis Milovanović, Emina I., 1958- Milentijević, Ivan, 1965- Stevanović, Dragan, 1974- Matejić, Marjan, 1977- Ćirić, Vladimir, 1977- http://creativecommons.org/licenses/by-nc-nd/3.0/at/legalcode srp