Matematične uganke v teoriji grafov

Javornik, Maja

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Title:	Matematične uganke v teoriji grafov
Authors:	ID Javornik, Maja (Author) ID Dravec, Tanja (Mentor) More about this mentor...
Files:	MAG_Javornik_Maja_2019.pdf (3,34 MB) MD5: 59F732B7D45A35840C1B5CABE739AC3A PID: 20.500.12556/dkum/19513fb6-9dc7-40d5-8c28-53e142724d26
Language:	Slovenian
Work type:	Master's thesis/paper
Typology:	2.09 - Master's Thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	V magistrskem delu je predstavljenih več učencem zanimivih matemati\v cnih ugank. Najprej obravnavamo različne matematične uganke skozi zgodovino vse od magi\v cnih kvadratov do ugank novej\v sega \v casa kot je rubikova kocka. Nato se osredotočimo na teorijo grafov in predstavimo ikozaedersko igro, problem Köningsber\v ski mostov, problem prečkanja reke brez mostov in problem \v stirih konjev. Kot uvod v obravnavo kitajskih prstanov predstavimo legendo o stolpu iz Brahme in vpeljemo Hanojske stolpe. Doka\v zemo optimalno re\v sitev Hanojskega stolpa z $n \in{\mathbb{N}}_0$ diski. Med drugimi predstavimo variacijo Hanojskega stolpa, ki se imenuje zamenjevalni Hanojski stolp in predstavimo zgodovino kitajskih prstanov. Nazadnje problem kitajskih prstanov podrobneje raziščemo in doka\v zemo formulo za najhitrejšo rešitev problema.
Keywords:	Kitajski prstani, Hanojski stolpi, Hamiltonovi grafi, Eulerjevi grafi, ravninski grafi
Place of publishing:	Maribor
Publisher:	[M. Javornik]
Year of publishing:	2019
PID:	20.500.12556/DKUM-75607
UDC:	519.17(043.2)
COBISS.SI-ID:	25074440
NUK URN:	URN:SI:UM:DK:CJYYMPU1
Publication date in DKUM:	23.01.2020
Views:	1650
Downloads:	231
Metadata:
Categories:	FNM
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Licences

License:	CC BY 4.0, Creative Commons Attribution 4.0 International

Link:	http://creativecommons.org/licenses/by/4.0/
Description:	This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:	14.12.2019

Secondary language

Language:	English
Title:	Mathematical puzzles in graph theory
Abstract:	The master’s thesis presents several interesting mathematical puzzles for students. First of all, we deal with various mathematical puzzles throughout the history – such as magic squares and puzzles of the recent times i.e. Rubik’s Cube. In the second part, emphasis is laid on graph theory, where we introduce, the icosian game, the Köningsberg Bridge problem, the problem of crossing the river without bridges, and the problem of four knights. As an introduction to the problem of Chinese rings, we present the legend of the Brahma tower and introduce the Hanoi towers. The optimal solution of the Tower of Hanoi problem with $n \in{\mathbb{N}}_0$ disks is proven. We also present a variation of Hanoi tower, called switching Tower of Hanoi, and the history of Chinese rings. Finally, we comprehensively investigate the problem of Chinese rings in detail and prove the formula for the fastest solution of the investigated problem.
Keywords:	Chinese rings, Tower of Hanoi, Hamiltonian graph, Euler graph, planar graph.

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