magistrsko delo
Janja Rebernik (Author), Aleksander Vesel (Mentor)

Abstract

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.

Keywords

benzenoidni grafi;katakondenzirani benzenoidni grafi;Fibonaccijeva dimenzija;1-faktor;resonančni grafi;magistrska dela;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [J. Rebernik]
UDC: 004.421.2:519.17(043.2)
COBISS: 22189832 Link will open in a new window
Views: 744
Downloads: 120
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Other data

Secondary language: English
Secondary title: Fibonacci dimension of the resonance graphs of catacondensed benzenoid graphs
Secondary abstract: 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 fifth part we describe an implementation of above mentioned algorithms in programming language C++ and show how it works on an example.
Secondary keywords: benzenoid graphs;catacondensed benzenoid graphs;Fibonacci dimension;1-factor;resonance graphs;master theses;
URN: URN:SI:UM:
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: IX, 47 f.
ID: 9136021