20.500.12556/DKUM-75607 Matematične uganke v teoriji grafov Mathematical puzzles in graph theory 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. 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. Kitajski prstani Hanojski stolpi Hamiltonovi grafi Eulerjevi grafi ravninski grafi Chinese rings Tower of Hanoi Hamiltonian graph Euler graph planar graph. true true false [M. Javornik] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2019-12-14 12:59:20 2020-01-23 13:18:27 2022-08-09 11:32:37 2020-01-24 03:12:19 2019 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17(043.2) 25074440 URN:SI:UM:DK:CJYYMPU1 MAG_Javornik_Maja_2019.pdf MAG_Javornik_Maja_2019.pdf 1 59F732B7D45A35840C1B5CABE739AC3A 2819c567c62e2ffbc0e530f48cc628a1b6cdbc18f2bafdcac69b9e00fcc0a13f 2d2bf47d-7c11-11eb-bb7a-00155d0001ca 20.500.12556/dkum/19513fb6-9dc7-40d5-8c28-53e142724d26 https://dk.um.si/Dokument.php?lang=slv&id=140059 Fakulteta za naravoslovje in matematiko 0 0 0