Title
Neki doprinosi spektralnoj teoriji grafova
Creator
Damnjanović, Ivan G., 1996-
CONOR:
110969609
Copyright date
2023
Object Links
Select license
Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
License description
Dozvoljavate samo preuzimanje i distribuciju dela, ako/dok se pravilno naznačava ime autora, bez ikakvih promena dela i bez prava komercijalnog korišćenja dela. Ova licenca je najstroža CC licenca. Osnovni opis Licence: http://creativecommons.org/licenses/by-nc-nd/3.0/rs/deed.sr_LATN. Sadržaj ugovora u celini: http://creativecommons.org/licenses/by-nc-nd/3.0/rs/legalcode.sr-Latn
Language
Serbian
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 1.7.2024.
Other responsibilities
Academic Expertise
Tehničko-tehnološke nauke
University
Univerzitet u Nišu
Faculty
Elektronski fakultet
Group
Katedra za matematiku
Alternative title
Some contributions to spectral graph theory
Publisher
[I. G. Damnjanović]
Format
128 listova
description
Biografija autora: list 128
Bibliografija: listovi 114-119
description
Graph Theory
Abstract (en)
The doctoral dissertation deals with solving three concrete scientific
problems from the field of spectral graph theory. First
of all, let a nut graph represent a nontrivial simple graph whose
adjacency matrix has a one dimensional null space all of whose
nonzero members contain no zero elements. The first resolved
scientific problem is the circulant nut graph existence problem
which is connected to determining all the pairs (n, d), n E
N, d E N0 for which there exists a d-regular circulant nut graph
of order n. Furthermore, let a balanced tree be a rooted tree all
of whose vertices from the same level have an equal number of
children. Also, for any d, k E N, d > 2, let the Bethe tree Bd, k
represent a balanced tree with k levels such that all of its vertices
outside the last level have exactly d - 1 children, and let
the dendrimer Dd, k be a balanced tree with k levels such that
all of its vertices outside the last level are of degree d. The second
scientific problem that the dissertation deals with is the
spectral analysis of balanced trees with a special focus on computing
the energy of Bethe trees and approximating the energy
of dendrimers. Finally, the goal of the third part of the doctoral
dissertation is to determine the energy of the newly introduced
martini graphs for the purpose of disproving a conjecture previously
disclosed by Akbari et al.
Authors Key words
spektar, karakteristični polinom, energija grafa, matičan graf, cirkulantan graf, ciklotomičan polinom, balansirano stablo, Bete stablo, dendrimer, martini graf
Authors Key words
spectrum, characteristic polynomial, graph energy, nut graph,
circulant graph, cyclotomic polynomial, balanced tree, Bethe
tree, dendrimer, martini graph
Classification
(510.22+519.17):(510.6+004.42)(043.3)
Subject
P110
Type
Tekst
Abstract (en)
The doctoral dissertation deals with solving three concrete scientific
problems from the field of spectral graph theory. First
of all, let a nut graph represent a nontrivial simple graph whose
adjacency matrix has a one dimensional null space all of whose
nonzero members contain no zero elements. The first resolved
scientific problem is the circulant nut graph existence problem
which is connected to determining all the pairs (n, d), n E
N, d E N0 for which there exists a d-regular circulant nut graph
of order n. Furthermore, let a balanced tree be a rooted tree all
of whose vertices from the same level have an equal number of
children. Also, for any d, k E N, d > 2, let the Bethe tree Bd, k
represent a balanced tree with k levels such that all of its vertices
outside the last level have exactly d - 1 children, and let
the dendrimer Dd, k be a balanced tree with k levels such that
all of its vertices outside the last level are of degree d. The second
scientific problem that the dissertation deals with is the
spectral analysis of balanced trees with a special focus on computing
the energy of Bethe trees and approximating the energy
of dendrimers. Finally, the goal of the third part of the doctoral
dissertation is to determine the energy of the newly introduced
martini graphs for the purpose of disproving a conjecture previously
disclosed by Akbari et al.
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