Lastne vrednosti grafa : diplomsko delo

Bolta, Sandra (author), Šparl, Primož (mentor)

V diplomskem delu obravnavamo linearne teorijo grafov. Zanimajo nas predvsem lastne vrednosti tako imenovanih matrik sosednosti danega grafa. V ta namen so v diplomskem delu predstavljeni tudi osnovni pojmi in nekateri rezultati linearne algebre, ter krajši uvod v teorijo grafov. Predstavljeni so pojmi matrike sosednosti, lastnih vrednosti ter spektra danega grafa. Obravnavana so vprašanja kako se lastnosti grafa odražajo na njegovem spektru. Izračunani so tudi spektri znanih družin grafov.

• Language: Slovenian
• Keywords: teorija grafov, matrika sosednosti, spekter grafa, standardne družine grafov
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Publisher: [S. Bolta]
• Year: 2014
• Number of pages: 34 str.
• PID: 20.500.12556/RUL-69252
• UDC: 519.17(043.2)
• COBISS.SI-ID: 10388297
• Publication date in RUL: 10.07.2015

BOLTA, Sandra, 2014, Lastne vrednosti grafa : diplomsko delo [online]. Bachelor’s thesis. S. Bolta. [Accessed 30 April 2025]. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=69252

Secondary language

• Language: English
• Title: Eigenvalues of a graph

Abstract

In this BSc thesis we deal with matrix graph theory. We are interested primarily in the eigenvalues of the so-called adjacency matrix of a given graph. Because of that, we present the basic concepts and some basic results from linear algebra and a short introduction to a graph theory. We introduce the concepts of adjacency matrices, eigenvalues and the spectrum of a given graph. We investigate how the properties of a given graph reflect on its spectrum. For the well-known families of graphs we calculated their spectra.