On integer domination in graphs and Vizing-like problems

Brešar, Boštjan; Henning, Michael A.; Klavžar, Sandi

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Title:	On integer domination in graphs and Vizing-like problems
Authors:	ID Brešar, Boštjan (Author) ID Henning, Michael A. (Author) ID Klavžar, Sandi (Author)
Files:	http://www.math.nthu.edu.tw/~tjm/myweb/FrameConAbs.htm
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	FERI - Faculty of Electrical Engineering and Computer Science
Abstract:	Nadaljujemo študij ${k}$ -dominantnih funkcij v grafih (ali, kot bomo tudi rekli, celoštevilske dominacije), ki so jo začeli Domke, Hedetniemi, Laskar in Fricke. Za celo število $k ge 1$ je funkcija $f: V(G) to {0,1,...,k}$ , definirana na točkah grafa $G$ , ${k}$ -dominantna funkcija, če je vsota funkcijskih vrednosti na vsaki zaprti okolici vsaj $k$ . Teža ${k}$ -dominantne funkcije je vsota funkcijskih vrednosti po vseh točkah. ${k}$ -dominantno število grafa $G$ je najmanjša teža ${k}$ -dominantne funkcije na $G$ . Obravnavamo ${k}$ -dominantno število kartezičnega produkta grafov, predvsem probleme povezane s slavno Vizingovo domnevo. Študirana je tudi povezava med ${k}$ -dominantnim številom in drugimi tipi dominacijskih parametrov.
Keywords:	matematika, teorija grafov, ${k}$ -dominantna funkcija, celoštevilska dominacija, Vizingova domneva, kartezični produkt grafov, mathematics, graph theory, ${k}$ -dominating function, integer domination, Vizing's conjecture, Cartesian product
Year of publishing:	2006
Number of pages:	str.1317-1328
Numbering:	Vol. 10, no. 5
PID:	20.500.12556/DKUM-51561
UDC:	519.17
ISSN on article:	1027-5487
COBISS.SI-ID:	14099545
NUK URN:	URN:SI:UM:DK:0SE3XNYN
Publication date in DKUM:	10.07.2015
Views:	1280
Downloads:	69
Metadata:
Categories:	Misc.
:	BREŠAR, Boštjan, HENNING, Michael A. and KLAVŽAR, Sandi, 2006, On integer domination in graphs and Vizing-like problems. Taiwanese journal of mathematics [online]. 2006. Vol. 10, no. 5, p. 1317–1328. [Accessed 2 April 2025]. Retrieved from: http://www.math.nthu.edu.tw/~tjm/myweb/FrameConAbs.htm Copy citation

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Title:	Taiwanese journal of mathematics
Shortened title:	Taiwan. j. math.
Publisher:	Mathematical Society of the Republic of China
ISSN:	1027-5487
COBISS.SI-ID:	13412872

Secondary language

Language:	Unknown
Title:	O celoštevilski dominaciji v grafih in problemih Vizingovega tipa
Abstract:	We continue the study of ${k}$ -dominating functions in graphs (or integer domination as we shall also say) started by Domke, Hedetniemi, Laskar, and Fricke. For $k ge 1$ an integer, a function $f: V (G) to {0,1,...,k}$ defined on the vertices of a graph $G$ is called a ${k}$ -dominating function if the sum of its function values over any closed neighborhood is at least k. $T$ he weight of a ${k}$ -dominating function is the sum of its function values over all vertices. The ${k}$ -domination number of $G$ is the minimum weightof a ${k}$ -dominating function of $G$ . We study the ${k}$ -domination number on the Cartesian product of graphs, mostly on problems related to the famous Vizing¡ s conjecture. A connection between the ${k}$ -domination number and other domination type parameters is also studied.

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