Lastnosti Laplaceovih matrik enostavnih in mešanih grafov

magistrsko delo

Saša Marolt (Author), Polona Oblak (Mentor)

Abstract

V magistrski nalogi obravnavamo spektralno teorijo enostavnih in mešanih grafov. Za Laplaceove matrike enostavnih grafov pokažemo, da je večkratnost lastne vrednosti nič enaka številu povezanih komponent grafa in preučimo celoštevilske lastne vrednosti Laplaceovih matrik dreves. Za mešane grafe pokažemo, da imajo Laplaceove matrike kvazidvodelnih grafov enak spekter kot Laplaceove matrike pripadajočih temeljnih enostavnih grafov. Predstavimo klasifikacijo vseh nesingularnih povezanih mešanih grafov na vsaj sedmih vozliščih, katerih Laplaceova matrika ima natanko dve lastni vrednosti večji od dve.

Keywords

Laplaceova matrika;enostavni grafi;mešani grafi;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.09 - Master's Thesis
Organization:	UL FRI - Faculty of Computer and Information Science
Publisher:	[S. Marolt]
UDC:	519.1
COBISS:	69014019
Views:	712
Downloads:	55
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Properties of Laplacian matrices of simple and mixed graphs
Secondary abstract:	In this work we discuss the spectral theory of simple and mixed graphs. For the Laplacian matrix of a simple graph we show that the multiplicity of the eigenvalue zero equals the number of connected components of the graph and we examine integer eigenvalues of the Laplacian matrix of a tree. For a mixed graph we show that the Laplacian matrix of a quasi-bipartite graph has the same spectrum as the Laplacian matrix of the corresponding underlying simple graph. We present the classification of all nonsingular connected mixed graphs on at least seven vertices whose Laplacian matrices have exactly two eigenvalues greater than two.
Secondary keywords:	Laplacian matrix;simple graphs;mixed graphs;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 2. stopnja
Pages:	IX, 47 str.
ID:	13099768