diplomsko delo
Eva Jug (Author), Sandi Klavžar (Mentor)

Abstract

V diplomskem delu se osredotočimo na Pellove grafe. Najprej predstavimo osnovne pojme s področja teorije grafov, nato pa še pomembnejše skupine grafov. Opišemo nekatere lastnosti Pellovih grafov ter jih obrazložimo. V poglavju 3 govorimo o lastnostih, ki so neposredno povezane z definicijo sosednosti v Pellovih grafih (dvodelnost, barvanje, prirejanje). Predstavimo kanonično dekompozicijo kot primer rekurzivne dekompozicije. V poglavju 4 opišemo lastnosti, povezane z razdaljami v grafu (polmer, premer, center, periferija). V poglavju 5 povežemo Pellove grafe s Fibonaccijevimi kockami, v poglavju 6 pa še s hiperkockami. V zadnjih dveh poglavjih podamo možno razlago za numerično identiteto, povezano s Fibonaccijevim številom, in vizualno predstavitev grafa Π_5.

Keywords

Pellov graf;Fibonaccijeva kocka;hiperkocka;dvodelen graf;medianski graf;interdisciplinarni študij;univerzitetni študij;diplomske naloge;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FRI - Faculty of Computer and Information Science
Publisher: [E. Jug]
UDC: 519.17:004(043.2)
COBISS: 163909379 Link will open in a new window
Views: 92
Downloads: 10
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Other data

Secondary language: English
Secondary title: Pell graph properties
Secondary abstract: This paper focuses on the Pell graphs. We begin by explaining the basic terminology from the field of graph theory and highlighting some of the more important classes of graphs. We describe several Pell graph properties with additional explanations. In Chapter 3 we talk about properties which are directly linked to the definition of neighbours in Pell graphs (bipartiteness, coloring, matching). We introduce the canonical decomposition as an example of recursive decomposition. In Chapter 4 we describe properties based on distances between vertices (radius, diameter, center, periphery). In Chapter 5 we connect Pell graphs to Fibonacci cubes and in Chapter 6 to hypercubes. In the last two chapters we give a possible explanation for a numerical identity, linked to the Fibonacci numbers, and a visual representation of the graph Π_5.
Secondary keywords: Pell graph;Fibonacci cube;hypercube;bipartite graph;median graph;computer science;computer and information science;computer science and mathematics;interdisciplinary studies;diploma;Teorija grafov;Matematika;Računalništvo;Univerzitetna in visokošolska dela;
Type (COBISS): Bachelor thesis/paper
Study programme: 1000407
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za računalništvo in informatiko
Pages: 43 str.
ID: 19904928