Algebarske metode u teoriji grafova

Kurtoić, Tomislav

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master's thesis

Algebarske metode u teoriji grafova

Zagreb: University of Zagreb, Faculty of Science, 2022. urn:nbn:hr:217:525638

Kurtoić, Tomislav

University of Zagreb
Faculty of Science
Department of Mathematics

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APA 6th Edition

Kurtoić, T. (2022). Algebarske metode u teoriji grafova (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:525638

MLA 8th Edition

Kurtoić, Tomislav. "Algebarske metode u teoriji grafova." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:525638

Chicago 17th Edition

Kurtoić, Tomislav. "Algebarske metode u teoriji grafova." Master's thesis, University of Zagreb, Faculty of Science, 2022. https://urn.nsk.hr/urn:nbn:hr:217:525638

Harvard

Kurtoić, T. (2022). 'Algebarske metode u teoriji grafova', Master's thesis, University of Zagreb, Faculty of Science, accessed 21 January 2025, https://urn.nsk.hr/urn:nbn:hr:217:525638

Vancouver

Kurtoić T. Algebarske metode u teoriji grafova [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2025 January 21] Available at: https://urn.nsk.hr/urn:nbn:hr:217:525638

IEEE

T. Kurtoić, "Algebarske metode u teoriji grafova", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:217:525638

Cite this item: https://urn.nsk.hr/urn:nbn:hr:217:525638

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Metadata

Title	Algebarske metode u teoriji grafova
Title (english)	Algebraic methods in graph theory
Author	Tomislav Kurtoić
Mentor	Slaven Kožić (mentor)
Committee member	Slaven Kožić (predsjednik povjerenstva)
Committee member	Ozren Perše (član povjerenstva)
Committee member	Željka Milin Šipuš (član povjerenstva)
Committee member	Zvonimir Bujanović (član povjerenstva)
Granter	University of Zagreb Faculty of Science (Department of Mathematics) Zagreb
Defense date and country	2022-09-27, Croatia
Scientific / art field, discipline and subdiscipline	NATURAL SCIENCES Mathematics
Abstract	Glavna svrha ovog rada je pokazati na koji način su povezana područja linearne algebre i teorije grafova te kako njihovu vezu možemo iskoristiti za rješavanje problema u stvarnom životu. U prvom poglavlju navodimo definicije, teoreme i rezultate iz linearne algebre i teorije grafova koji su nužni za shvaćanje glavnog dijela rada. Drugo, treće i četvrto poglavlje bavi se proučavanjem matrice susjedstva, matrice incidencije i Laplaceove matrice. Definiramo svaku od navedenih matrica, na stvarnim primjerima prikazujemo načine njihovog određivanja te prezentiramo njihove primjene u proučavanju pripadnih grafova. U petom i šestom poglavlju promatramo matricu udaljenosti stabla i matricu otpora. Definiramo navedene matrice i proučavamo njihova svojstva i primjene. Poseban naglasak je dan na rezultate vezane uz njihove svojstvene vrijednosti, determinante i povezanosti s Laplaceovom matricom.
Abstract (english)	The main purpose of this thesis is to show the connections between linear algebra and graph theory and their applications to solving real life problems. In the first chapter we give basic definitions, theorems and results from linear algebra and graph theory which are vital for further understanding of the thesis. In chapters two, three and four we are focused on adjacency and incidence matrices along with the Laplacian matrix. We define each of these matrices, we show how to determine them by using real life examples and we present their applications to the study of the underlying graphs. In the last two chapters, chapters five and six, we examine the distance matrix of a tree and the resistance matrix. We introduce the aforementioned matrices and study their properties and applications. Special emphasis is given to the results concerning their eigenvalues, determinants and connections with the Laplacian matrix.
Keywords
Keywords (english)
Language	croatian
URN:NBN	urn:nbn:hr:217:525638
Study programme	Title: Mathematics Education; specializations in: Mathematics Education Course: Mathematics Education Study programme type: university Study level: graduate Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resource	Text
File origin	Born digital
Access conditions	Open access
Terms of use
Repository	Repository of the Faculty of Science
Created on	2022-10-28 10:01:17