Uporaba teorije grafov pri igrah in drugih realnih problemih

diplomsko delo

Matic Ber (Author), Marko Jakovac (Mentor)

Abstract

V diplomskem delu so opisane miselne igre, katerih rešitve lahko naravno podamo s pomočjo teorije grafov. Pogledamo nekaj najbolj znanih zagonetk in jih predstavimo v obliki dobro raziskanih ter znanih grafov. Ti med drugimi vključujejo polne dvodelne grafe, hiperkocke in zgodovinsko znan graf Königsbergških mostov. Vpeljemo možno posplošitev zagonetk na poljubno dimenzijo in podamo zmagovalno strategijo. V delu se podrobneje obravnavajo tudi določeni gospodarski problemi in uporaba teorije grafov v realnem svetu na različnih področjih kot so optimizacijski problemi, minimiziranje cene v ekonomiji, problemi v prometu in teoriji koristnosti. Postavimo vprašanje, ali ima izbran problem sprejemljivo rešitev in če je možno, predlagamo algoritem, ki privede do rešitve.

Keywords

diplomska dela;teorija grafov;miselne igre;Eulerjevi grafi;Hamiltonovi grafi;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Ber]
UDC:	519.17(043.2)
COBISS:	22745864
Views:	1429
Downloads:	183
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Graph theory with applications in games and other real problems
Secondary abstract:	In the following thesis we describe a set of playable mind games that lend themselves to an elegant transfiguring in the form of a graph. By means of graph theory, we are able to convert some of the most well-known brain teasers and re-imagine them as famous graphs. These among others include bipartite graphs, hypercubes and a historically famous Königsberg bridge graph. We provide the means of generalizing the aforementioned games to an arbitrary dimension, and also contribute a winning strategy in conceived situations. We take a closer look at the application of graph theory to solving real-world problems in fields ranging from route optimization, cost reductions, to tra c and utility related problems. If an e cient solution for a given problem exists, we suggest an algorithm that confers a solution.
Secondary keywords:	theses;graph theory;puzzles;Eulerian graphs;Hamiltonian graphs;Univerzitetna in visokošolska dela;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	51 f.
ID:	9164763