Obravnava barvanj grafov in tetivnih grafov v srednješolskem izobraževanju

magistrsko delo

Jasmina Ferme (Author), Boštjan Brešar (Mentor), Alenka Lipovec (Co-mentor)

Abstract

V magistrskem delu obravnavamo izbrane vsebine s področja teorije grafov, te so barvanje vozlišč grafov, tetivni grafi in grafi intervalov. V prvem delu navedemo vse potrebne definicije, trditve in izreke skupaj z dokazi. Podamo več karakterizacij tetivnih grafov in grafov intervalov, kjer se osredotočamo na obravnavo z vidika presečnih grafov. Navedene vsebine tudi povezujemo in odkrivamo zveze med njimi, posvetimo se predvsem barvanju tetivnih grafov in grafov intervalov. V drugem delu magistrskega dela podajamo primer obravnave navedenih vsebin v srednješolskem izobraževanju; vključimo tudi obravnavo vsebine uvod v teorijo grafov ter vsebine, ki združuje navedeno. Vsebine podajamo v obliki vsebinsko-metodičnih priprav na poučevanje, v sklopu katerih predlagamo tudi učne oblike in metode, učne pripomočke in časovni razpored aktivnosti ter navajamo matematična znanja, ki jih dijaki razvijajo tekom učnih ur. Podajamo teoretične osnove nekaterih didaktični elementov ter navajamo načela, s katerimi je poučevanje po pripravah usmerjeno in cilje, ki jih uresničuje.

Keywords

barvanje vozlišč grafov;tetivni grafi;grafi intervalov;teorija grafov v srednješolskem izobraževanju;magistrska dela;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[J. Ferme]
UDC:	37.091.3:519.17(043.2)
COBISS:	22411272
Views:	1169
Downloads:	278
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Graph colorings and chordal graphs in secondary school education
Secondary abstract:	In this Master's thesis, we discuss chosen topics of graph theory. These are: vertex colouring, chordal graphs and interval graphs. In the first part, we list all of the necessary definitions, claims and theorems together with their proofs. We provide additional characterization of chordal and interval graphs. We focus on discussing them from the intersection graphs' viewpoint. We connect all of the topics and we search for relations between them. We focus on chordal graphs colouring and interval graphs colouring. In the second part, we provide example of discussing above-mentioned topics in secondary education. We also add discussion about introduction into graph theory and the topic, which combines all of the mentioned topics. Topics are presented in the form of content and methods based lesson plan. We suggest teaching forms, methods, materials, aids, time schedule for activities and we list mathematical knowledge that students develop during the lessons. We introduce theoretical base of some didactics elements, we list principles which help us direct our teaching and goals which are realized.
Secondary keywords:	vertex coloring;chordal graphs;interval graphs;graph theory in secondary education;master theses;
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, 120 f.
ID:	9151499