Grafi, ki dosežejo enakost v Vizingovi domnevi

magistrsko delo

Anamarija Lakner (Author), Boštjan Brešar (Mentor)

Abstract

Vizing je leta 1968 postavil domnevo, da je dominantno število kartezičnega produkta dveh grafov večje ali enako produktu njunih dominantnih števil. V magistrskem delu obravnavamo družine grafov, ki v tej domnevi dosežejo enakost. V prvem delu magistrskega dela smo navedli pojme in trditve, ki jih potrebujemo za razumevanje glavnega problema naloge. Drugo poglavje se nanaša na različne meje dominantnega števila kartezičnega produkta dveh grafov in družine grafov, ki zadoščajo Vizingovi domnevi. V tretjem poglavju obravnavamo družine grafov, ki pod določenimi pogoji dosežejo enakost v Vizingovi domnevi, ter znane rezultate podamo v preglednici.

Keywords

magistrska dela;dominantno število;dominantna množica;Vizingova domneva;enakost v Vizingovi domnevi;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[A. Lakner]
UDC:	519.17(043.2)
COBISS:	127467779
Views:	2
Downloads:	0
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Graphs achieving the equality in vizing's conjecture
Secondary abstract:	In 1963, Vizing conjectured that the domination number of the Cartesian product of two graphs is greater or equal to the product of their domination numbers. In this masters thesis, we discuss graph classes that achieve equality in this conjecture. In the first part, we list all the necessary definitions and theorems that are needed for understanding the main problem of the thesis. In the second part, we present different bounds for the domination number of the Cartesian product of two graphs and graph classes that satisfy Vizingʹs conjecture. In the third part, we study graph classes that under various conditions satisfy the equality in Vizingʹs conjecture and present known results in a table.
Secondary keywords:	master theses;domination number;domination set;Vizing’s conjecture;equality in Vizingʹs conjecture;Grafične metode;Univerzitetna in visokošolska dela;
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	VIII, 54 f.
ID:	16500831