magistrsko delo
Nina Črešnjevec (Author), Tanja Gologranc (Mentor)

Abstract

V magistrskem delu obravnavamo različne tipe dominacij, in sicer dominantno število, ne odvisnostno število, neodvisno dominantno število in zgornje dominantno število. Neodvisno dominantno število je raziskano na različnih družinah grafov kot tudi na različnih grafovskih produktih. V prvem delu magistrskega dela smo navedli vse pojme, trditve, izreke, ki jih potrebujemo za razumevanje glavnega problema magistrskega dela. Predstavimo tudi različne razrede grafov in različne dominacije v grafih. V drugem poglavju obravnavamo različne meje neodvisnega dominantnega števila. Predstavljene so splošne meje, ki veljajo na različnih družinah grafov in meje, ki veljajo za dvodelne grafe. Tretje poglavje pa se nanaša na neodvisno dominantno število krepkega, korenskega in kartezičnega produkta. Za nekatere od teh produktov smo prikazali tudi rezultate o ne odvisnostnem številu in dominantnem številu.

Keywords

magistrska dela;dominantno število;neodvisno dominantno število;neodvisnostno število;dominantno popolni grafi;dobro pokriti grafi;grafovski produkti;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [N. Črešnjevec]
UDC: 519.17(043.2)
COBISS: 23904008 Link will open in a new window
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Other data

Secondary language: English
Secondary title: Independent domination in graphs
Secondary abstract: In this Master's thesis, we discuss different invariants in domination theory. These are: domination number, independent domination number, independence number, upper domination number. We study independent domination number on different graph classes and devote one chapter to independent domination number of graph products. In the first part we list all necessary defnitions, claims and theorems that are needed in the rest of the thesis. We present and define different graph classes and different types of dominations. In the second part we present some bounds for independent domination number in general graphs and also in special graph classes such as bipartite graphs. In the third part we study independent domination number of strong product, rooted product and Cartesian product. For some of those graph products we present also the results on independence and domination number.
Secondary keywords: master theses;domination number;independent domination number;independence number;domination perfect graphs;well covered graphs;product graphs;
URN: URN:SI:UM:
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: IX, 55 f.
ID: 10873363