Vennovi diagrami

diplomsko delo

Nina Plošnik (Author), Matjaž Kovše (Mentor)

Abstract

Diplomsko delo obravnava Vennove diagrame. Osrednja tema so splošni Vennovi diagrami in grafi, ki so povezani z Vennovimi diagrami. V uvodnem poglavju predstavimo osnovne definicije iz teorije grafov, ki jih potrebujemo v nadaljevanju, definiramo Vennove diagrame in povemo nekaj o njihovi uporabi in o primerjavi z Eulerjevimi diagrami. V drugem poglavju prikažemo obstoj Vennovih diagramov za n%3 na primerih dveh konstrukcij in pokažemo, kdaj se jih lahko nariše z uporabo skladnih krogov. V zadnjem poglavju podrobno obravnavamo grafe, ki so povezani z Vennovimi diagrami. Najprej predstavimo Vennove duale, definiramo, kdaj so Vennovi diagrami izomorfni, in obravnavamo Vennove diagrame in Vennove razrede. Nato raziščemo razširitev Vennovega diagrama in podamo Winklerjevo domnevo, ki pa ostaja nepotrjena. Z odpravo omejitve enostavnosti v nadaljevanju dokažemo Grünbaumov izrek. Na koncu poglavja obravnavamo tudi minimalne in monotone Vennove diagrame.

Keywords

matematika;diagrami;grafi;izomorfizem;dvodelni grafi;ravninski grafi;polni grafi;kartezični produkt;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[N. Plošnik]
UDC:	51(043.2)
COBISS:	18719752
Views:	3396
Downloads:	147
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	VENN DIAGRAMS
Secondary abstract:	The diploma thesis focuses on Venn diagrams. The main themes are the general Venn diagrams and graphs associated with Venn diagrams. The first part examines basic definitions from the graph theory and introduces the use of Venn diagrams, which are further compared to Euler diagrams. It focuses on the definition of Venn diagrams. In the next part Venn diagrams existence for n%3 is shown using two different constructions. It also presents how these constructions can be drawn by the use of congruent circles. In the last part graphs associated to Venn diagrams are discussed in details. First it presents Venn dual graphs, defines when they are isomorphic and deals with Venn diagrams and classes. Then it explores extension of Venn diagram and gives Winkler's conjecture, which remains unproven. By eliminating restrictions of simplicity it further proves Grünbaum's theorem. In the end it also focuses on minimal and monotone Venn diagram.
Secondary keywords:	Venn diagram;Euler diagram;isomorphism of graphs;bipartite graph;planar graph;planar dual graph;complete graph;Cartesian product of graphs;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	45 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19552