Celotna in neodvisna mavrična dominacija

na študijskem programu 2. stopnje Matematika

Anja Petek (Author), Aleksandra Tepeh (Mentor)

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

magistrska dela;dominacija;kartezični produkt;mavrična dominacija;celotna mavrična dominacija;neodvisna mavrična dominacija;Nordhaus-Gaddum;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[A. Tepeh]
UDC:	519.17(043.2)
COBISS:	92029955
Views:	400
Downloads:	32
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Total and independent rainbow domination
Secondary 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 ▫$G$▫.
Secondary keywords:	master theses;domination;Cartesian product;rainbow domination;total rainbow domination;independent rainbow domination;Nordhaus-Gaddum;Teorija grafov;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:	X, 61 f.
ID:	13345146