Celotna in neodvisna mavrična  dominacija : na študijskem programu 2. stopnje Matematika

Petek, Anja

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Title:	Celotna in neodvisna mavrična dominacija : na študijskem programu 2. stopnje Matematika
Authors:	ID Petek, Anja (Author) ID Tepeh, Aleksandra (Mentor) More about this mentor...
Files:	MAG_Petek_Anja_2021.pdf (618,19 KB) MD5: FC5BBE977A5DDA0D05C135F8E2EBF58C PID: 20.500.12556/dkum/de51b8b1-6b61-410b-a212-e494c4038a25
Language:	Slovenian
Work type:	Master's thesis/paper
Typology:	2.09 - Master's Thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	V magistrskem delu predstavimo novi različici mavrične dominacije, celotno in neodvisno mavrično dominacijo. Podobno kot pri mavrični dominaciji sta tudi ti dve inačici povezani s posplošenimi prizmami $G\square K_k$ . Slednje predstavljajo kartezični produkt poljubnega grafa $G$ in polnega grafa $K_k$ . V delu podamo nekaj mej in lastnosti $k$ -mavričnega celotnega dominantnega števila $\gamma_{\rtk}(G)$ , ter $k$ -mavričnega neodvisnega dominantnega števila $\gamma_{\rik}(G)$ . Za nekatere znane družine grafov predstavimo tudi natančne vrednosti. Na koncu dela sledi Nordhaus-Gaddumov tip rezultata neodvisne mavrične dominacije za $k=2$ , $5\leq \gamma_{\ridva}(G)+\gamma_{\ridva}(\overline{G})\leq n+3$ , kjer $\overline{G}$ predstavlja komplement grafa $G$ .
Keywords:	dominacija, kartezični produkt, mavrična dominacija, celotna mavrična dominacija, neodvisna mavrična dominacija, Nordhaus-Gaddum
Place of publishing:	Maribor
Place of performance:	Maribor
Publisher:	[A. Tepeh]
Year of publishing:	2021
Number of pages:	X, 61 f.
PID:	20.500.12556/DKUM-80452
UDC:	519.17(043.2)
COBISS.SI-ID:	92029955
Publication date in DKUM:	05.01.2022
Views:	914
Downloads:	58
Metadata:
Categories:	FNM
:	PETEK, Anja, 2021, Celotna in neodvisna mavrična dominacija : na študijskem programu 2. stopnje Matematika [online]. Master’s thesis. Maribor : A. Tepeh. [Accessed 22 April 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=80452 Copy citation

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Licences

License:	CC BY 4.0, Creative Commons Attribution 4.0 International

Link:	http://creativecommons.org/licenses/by/4.0/
Description:	This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:	13.09.2021

Secondary language

Language:	English
Title:	Total and independent rainbow domination
Abstract:	In Master's thesis we study two new rainbow domination invariants, total and independent rainbow domination. Like rainbow domination, these two versions are also connected with generalized prisms $G\square K_k$ . The latter ones represent the Cartesian product of any graph $G$ and a complete graph $K_k$ . In the thesis we give some bounds and properties of the $k$ -rainbow independent domination number $\gamma_{\rtk}(G)$ and the $k$ -rainbow total domination number $\gamma_{\rik}(G)$ . For some families of graphs we also give exact values. At the end of this work we prove a Nordhaus-Gaddum type of result of independent rainbow domination for $k=2$ , $5\leq \gamma_{\ridva}(G)+\gamma_{\ridva}(\overline{G})\leq n+3$ , where $\overline{G}$ represents the complement of a graph $G$ .
Keywords:	domination, Cartesian product, rainbow domination, total rainbow domination, independent rainbow domination, Nordhaus-Gaddum

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