o:2616 Neki doprinosi spektralnoj teoriji grafova Some contributions to spectral graph theory : doctoral dissertation sr 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 91552100 138833929 91552101 8704 2024-09-03T15:59:46.053Z 45 no 46 Ivan G., 1996- Damnjanović 110969609 2023 63 mentor Emina I., 1958- Milovanović 13796455 2023 63 član komisije Ivan, 1965- Milentijević 6254439 2023 63 član komisije Dragan, 1974- Stevanović 13819751 2023 63 član komisije Marjan, 1977- Matejić 5909351 2023 63 član komisije Vladimir, 1977- Ćirić 11384679 2023 128 listova 1513732 http://phaidrani.ni.ac.rs/o:2616 no yes 12 2024-09-03T15:59:46.320Z 70 spektar, karakteristični polinom, energija grafa, matičan graf, cirkulantan graf, ciklotomičan polinom, balansirano stablo, Bete stablo, dendrimer, martini graf spectrum, characteristic polynomial, graph energy, nut graph,circulant graph, cyclotomic polynomial, balanced tree, Bethetree, dendrimer, martini graph (510.22+519.17):(510.6+004.42)(043.3) P110 1738 18A03 18A0304 2023