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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

Institutional repository: Repository of the Faculty of Science

Cite this document

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

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

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

Kurtoić, T. (2022). 'Algebarske metode u teoriji grafova', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:525638

Kurtoić T. Algebarske metode u teoriji grafova [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2022 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:525638

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

Metadata
TitleAlgebarske metode u teoriji grafova
Title (english)Algebraic methods in graph theory
AuthorTomislav Kurtoić
MentorSlaven Kožić (mentor)
Committee memberSlaven Kožić (predsjednik povjerenstva)
Committee memberOzren Perše (član povjerenstva)
Committee memberŽeljka Milin Šipuš (član povjerenstva)
Committee memberZvonimir Bujanović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2022-09-27, 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)
Languagecroatian
URN:NBNurn:nbn:hr:217:525638
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-10-28 10:01:17