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Title:
Grafi, ki dosežejo enakost v vizingovi domnevi : magistrsko delo
Authors:
ID
Lakner, Anamarija
(Author)
ID
Brešar, Boštjan
(Mentor)
More about this mentor...
Files:
MAG_Lakner_Anamarija_2022.pdf
(568,89 KB)
MD5: C8346B452984403A309DF0BC42573DB3
Language:
Slovenian
Work type:
Master's thesis/paper
Typology:
2.09 - Master's Thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
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 magistrske naloge 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 tabeli.
Keywords:
dominantno število
,
dominantna množica
,
Vizingova domneva
,
enakost v Vizingovi domnevi
Place of publishing:
Maribor
Place of performance:
Maribor
Publisher:
[A. Lakner]
Year of publishing:
2022
Number of pages:
VIII, 54 f.
PID:
20.500.12556/DKUM-83117
UDC:
519.17(043.2)
COBISS.SI-ID:
127467779
Publication date in DKUM:
28.10.2022
Views:
573
Downloads:
54
Metadata:
Categories:
FNM
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:
LAKNER, Anamarija, 2022,
Grafi, ki dosežejo enakost v vizingovi domnevi : magistrsko delo
[online]. Master’s thesis. Maribor : A. Lakner. [Accessed 13 April 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=83117
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Licences
License:
CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:
http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:
The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:
19.09.2022
Secondary language
Language:
English
Title:
Graphs achieving the equality in vizing's conjecture : na študijskem programu 2. stopnje Matematika
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 master’s 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 Vizing’s conjecture. In the third part, we study graph classes that under various conditions satisfy the equality in Vizing’s conjecture and present known results in a table.
Keywords:
domination number
,
domination set
,
Vizing’s conjecture
,
equality in Vizing’s conjecture
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