izpis_h1_title_alt

Neenakosti Nordhaus-Gaddumovega tipa lastnih vrednosti Laplaceove matrike : magistrsko delo
ID Lučovnik, Tilen (Author), ID Oblak, Polona (Mentor) More about this mentor... This link opens in a new window

.pdfPDF - Presentation file, Download (736,09 KB)
MD5: 12066DEFA6329F51257D1ADE2F200957

Abstract
Enostavnemu grafu $G$ z $n$ vozlišči definiramo matriko sosednosti in Laplaceovo matriko. Obe imata realne lastne vrednosti. Lastne vrednosti matrike sosednosti označimo s $\theta_1(G) \geq \cdots \geq \theta_n(G)$, lastne vrednosti Laplaceove matrike pa z $\lambda_1(G) \geq \cdots \geq \lambda_n(G) = 0$. V delu študiramo neenakosti Nordhaus-Gaddumovega tipa za lastne vrednosti matrike sosednosti in Laplaceove matrike. To so omejitve na vsote oblik $\theta_i(G) + \theta_i(\overline{G})$ in $\lambda_j(G) + \lambda_j(\overline{G})$ za določene vrednosti indeksov $i$ in $j$, pri čemer je $\overline{G}$ komplement grafa $G$. Posebej se osredotočimo na preučevanje vsot za najmanjšo lastno vrednost matrike sosednosti in največji dve lastni vrednosti Laplaceove matrike.

Language:Slovenian
Keywords:neenakosti Nordhaus-Gaddumovega tipa, matrika sosednosti, Laplaceova matrika, lastne vrednosti, algebraična povezanost
Work type:Master's thesis/paper
Typology:2.10 - Specialist Thesis
Organization:FMF - Faculty of Mathematics and Physics
Year:2021
PID:20.500.12556/RUL-127506 This link opens in a new window
UDC:519.1
COBISS.SI-ID:66285571 This link opens in a new window
Publication date in RUL:11.06.2021
Views:921
Downloads:64
Metadata:XML RDF-CHPDL DC-XML DC-RDF
:
Copy citation
Share:Bookmark and Share

Secondary language

Language:English
Title:Nordhaus-Gaddum type inequalities for Laplacian eigenvalues
Abstract:
For a simple graph $G$ of order $n$, we define its adjacency matrix and Laplacian matrix. Both have real eigenvalues. Let $\theta_1(G) \geq \cdots \geq \theta_n(G)$ be the eigenvalues of the adjacency matrix and $\lambda_1(G) \geq \cdots \geq \lambda_n(G) = 0$ the eigenvalues of the Laplacian matrix of graph $G$. We study Nordhaus-Gaddum type inequalities for the eigenvalues of these two matrices. These are upper and lower bounds for sums of the forms $\theta_i(G) + \theta_i(\overline{G})$ and $\lambda_j(G) + \lambda_j(\overline{G})$, where $\overline{G}$ denotes the graph complement of $G$. The focus of this work is on the sums for the smallest eigenvalue of the adjacency matrix and the largest two eigenvalues of the Laplacian matrix.

Keywords:Nordhaus-Gaddum type inequalities, adjacency matrix, Laplacian matrix, eigenvalues, algebraic connectivity

Similar documents

Similar works from RUL:
Similar works from other Slovenian collections:

Back