Simetrični bicirkulanti

Abstract

Keywords

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Language:	Slovenian
Year of publishing:	2014
Source:	Ljubljana
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[G. Vasiljević]
UDC:	519.17(043.2)
COBISS:	10289225
Views:	978
Downloads:	171
Average score:	0 (0 votes)
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Secondary language:	English
Secondary title:	Symmetric bicirculants
Secondary abstract:	This BSc thesis deals with certain topics from graph theory. When we talk about studying graphs, we usually mean studying their structure and their structural properties. By doing that, we are often interested in automorphisms of a graph (symmetries), which are permutations of its vertex set, preserving adjacency. There exist graphs, which are symmetric enough, so that automorhism group acts transitively on their vertex set. This means that for any pair of vertices of the graph, there is an automorphism, mapping one vertex to the other. Such graphs are called vertex-transitive. Similarly, a graph is edge-transitive, if its automorphism group acts transitively on its edge set and is arc-transitive, if its automorphism group acts transitively on its arc set. A bicirculant is a graph, which admits an automorhpism with two orbits of the same length. When studying bicirculants, one of the goals is to classify or at least identify infinite families of vertex-, edge- or arc-transitive bicirculants, given additional restrictions, such as the degree of vertices. In this thesis, we will examine the results of Frucht, Graver and Watkins, who studied the so-called Generalised Petersen graphs (cubic bicirculants) and classified the vertex- and edge-transitive ones. The next natural step is to study the natural generalizations of Generalised Petersen graphs, the so-called Rose-window graphs. The first to study them was Wilson, who also identified four families of edge-transitive Rose-window graphs. The main focus of this thesis is on Wilson's work. We present four families of Rose-Window graphs from Wilson's paper and show, that their members are in fact edge-transitive bicirculants.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Matematika in računalništvo
Pages:	39 str.
ID:	8701148