Global ETD Search

1	Spectra of Normalized Laplace Operators for Graphs and Hypergraphs Mulas, Raffaella 25 June 2020 (has links) In this thesis, we bring forward the study of the spectral properties of graphs and we extend this theory for chemical hypergraphs, a new class of hypergraphs that model chemical reaction networks. info:eu-repo/classification/ddc/500 ddc:500
2	A Nordhaus-Gaddum Type Problem for the Normalized Laplacian Spectrum and Graph Cheeger Constant Knudson, Adam Widtsoe 21 June 2024 (has links) (PDF) We will study various quantities related to connectivity of a graph. To this end, we look at Nordhaus-Gaddum type problems, which are problems where the same quantity is studied for a graph $G$ and its complement $G^c$ at the same time. For a graph $G$ on $n$ vertices with normalized Laplacian eigenvalues $0 = \lambda_1(G) \leq \lambda_2(G) \leq \cdots \leq \lambda_n(G)$ and graph complement $G^c$, we prove that \begin{equation} \max\{\lambda_2(G),\lambda_2(G^c)\}\geq \frac{2}{n^2}. \end{equation} We do this by way of lower bounding $\max\{i(G), i(G^c)\}$ and $\max\{h(G), h(G^c)\}$ where $i(G)$ and $h(G)$ denote the isoperimetric number and Cheeger constant of $G$, respectively. We also discuss some related Nordhaus-Gaddum questions. Normalized Laplacian Nordhaus-Gaddum problems Laplacian spread algebraic connectivity isoperimetric number Cheeger constant Physical Sciences and Mathematics
3	Égalités et inégalités géométriques pour les valeurs propres du laplacien et de Steklov Métras, Antoine 08 1900 (has links) No description available. Géométrie spectrale Spectre du laplacien Poblème de Dirichlet Problème de Steklov Constante de Cheeger Constante de Jammes-Cheeger Masse de Neumann Spectral geometry Laplace spectrum Dirichlet problem Steklov problem Cheeger constant Jammes-Cheeger constant Neumann mass

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