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1. Rebernik, Janja. Fibonaccijeva dimenzija resonančnih grafov katakondenziranih benzenoidnih grafov.

Degree: 2016, Univerza v Mariboru

Tema magistrskega dela je Fibonaccijeva dimenzija resonančnih grafov katakondenziranih benzenoidnih grafov. V delu predstavimo katakondenzirane benzenoidne grafe in problem določitve Fibonaccijeve dimenzije grafa, pri tem namenimo posebno pozornost določitvi Fibonaccijeve dimenzije resonančnih grafov katakondenziranih benzenoidnih grafov, za katere je opisan in implementiran tudi algoritem, ki izračuna Fibonaccijevo dimenzijo. V sklopu magistrskega dela je predstavljen in implementiran tudi algoritem, ki določi kanonično vložitev resonančnega grafa katakondenziranega benzenoidnega grafa v hiperkocko. Delo je razdeljeno na pet delov. V prvem delu so opisani osnovni pojmi in definicije. V drugem delu so predstavljeni katakondenzirani benzenoidni grafi in algoritem, ki določi kanonično vložitev resonančnega grafa katakondenziranega benzenoidnega grafa v hiperkocko. V tretjem delu je predstavljen problem določitve Fibonaccijeve dimenzije grafa. V četrtem delu pa ta problem omejimo na katakondenzirane benzenoidne grafe ter predstavimo algoritem za izračun Fibonaccijeve dimenzije resonančnih grafov katakondenziranih benzenoidnih grafov, ki ima linearno časovno zahtevnost. V petem delu opišemo implementacijo omenjenih algoritmov v programskem jeziku C++ in na primeru pokažemo delovanje programa.

This thesis focuses on the Fibonacci dimension of the resonance graphs of catacondensed benzenoid graphs. In the work we present catacondensed benzenoid graphs and the problem of determining the Fibonacci dimension of a graph. We pay special attention to the Fibonacci dimension of the resonance graphs of catacondensed benzenoid graphs, for which the algorithm for computing the Fibonacci dimension is described and implemented. In the work we also present and implement an algorithm for computing canonical codes of the resonance graph of the catacondensed benzenoid graph. This master thesis is divided into five parts. In the first part we describe basic concepts and definitions. In the second part, catacondensed benzenoid graphs are presented and algorithm for calculating canonical codes of their resonance graphs. In the third part we describe the problem of determining the Fibonacci dimension of a graph. In the fourth part we restrict this problem on catacondensed benzenoid graphs. We also present a linear algorithm for determining the Fibonacci dimension of the resonance graphs of catacondensed benzenoid graphs. In the _fth part we describe an implementation of above mentioned algorithms in programming language C++ and show how it works on an example.

Advisors/Committee Members: Vesel, Aleksander.

Subjects/Keywords: benzenoidni graf; katakondenzirani benzenoidni graf; Fibonaccijeva dimenzija; 1-faktor; resonančni graf; benzenoid graph; catacondensed benzenoid graph; Fibonacci dimension, 1-factor; resonance graph; info:eu-repo/classification/udc/004.421.2:519.17(043.2)

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APA (6th Edition):

Rebernik, J. (2016). Fibonaccijeva dimenzija resonančnih grafov katakondenziranih benzenoidnih grafov. (Masters Thesis). Univerza v Mariboru. Retrieved from https://dk.um.si/IzpisGradiva.php?id=58294 ; https://dk.um.si/Dokument.php?id=88563&dn= ; https://plus.si.cobiss.net/opac7/bib/22189832?lang=sl

Chicago Manual of Style (16th Edition):

Rebernik, Janja. “Fibonaccijeva dimenzija resonančnih grafov katakondenziranih benzenoidnih grafov.” 2016. Masters Thesis, Univerza v Mariboru. Accessed September 22, 2019. https://dk.um.si/IzpisGradiva.php?id=58294 ; https://dk.um.si/Dokument.php?id=88563&dn= ; https://plus.si.cobiss.net/opac7/bib/22189832?lang=sl.

MLA Handbook (7th Edition):

Rebernik, Janja. “Fibonaccijeva dimenzija resonančnih grafov katakondenziranih benzenoidnih grafov.” 2016. Web. 22 Sep 2019.

Vancouver:

Rebernik J. Fibonaccijeva dimenzija resonančnih grafov katakondenziranih benzenoidnih grafov. [Internet] [Masters thesis]. Univerza v Mariboru; 2016. [cited 2019 Sep 22]. Available from: https://dk.um.si/IzpisGradiva.php?id=58294 ; https://dk.um.si/Dokument.php?id=88563&dn= ; https://plus.si.cobiss.net/opac7/bib/22189832?lang=sl.

Council of Science Editors:

Rebernik J. Fibonaccijeva dimenzija resonančnih grafov katakondenziranih benzenoidnih grafov. [Masters Thesis]. Univerza v Mariboru; 2016. Available from: https://dk.um.si/IzpisGradiva.php?id=58294 ; https://dk.um.si/Dokument.php?id=88563&dn= ; https://plus.si.cobiss.net/opac7/bib/22189832?lang=sl

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