Search results
Results from the WOW.Com Content Network
Spectral graph theory emerged in the 1950s and 1960s. Besides graph theoretic research on the relationship between structural and spectral properties of graphs, another major source was research in quantum chemistry , but the connections between these two lines of work were not discovered until much later. [ 15 ]
Fan-Rong King Chung Graham (Chinese: 金芳蓉; pinyin: Jīn Fāngróng; born October 9, 1949), known professionally as Fan Chung, is a Taiwanese-born American mathematician who works mainly in the areas of spectral graph theory, extremal graph theory and random graphs, in particular in generalizing the Erdős–Rényi model for graphs with general degree distribution (including power-law ...
Fan Chung has developed an extensive theory using a rescaled version of the Laplacian, eliminating the dependence on the number of vertices, so that the bounds are somewhat different. [ 7 ] In models of synchronization on networks, such as the Kuramoto model , the Laplacian matrix arises naturally, so the algebraic connectivity gives an ...
This quantity is studied in the context of spectral graph theory. More precisely, let G be a graph with n vertices. It is assumed that G is a simple graph, that is, it does not contain loops or parallel edges. Let A be the adjacency matrix of G and let , =, …,, be the eigenvalues of A. Then the energy of the graph is defined as:
This type of mapping between graphs is the one that is most commonly used in category-theoretic approaches to graph theory. A proper graph coloring can equivalently be described as a homomorphism to a complete graph. 2. The homomorphism degree of a graph is a synonym for its Hadwiger number, the order of the largest clique minor. hyperarc
The name spectral theory was introduced by David Hilbert in his original formulation of Hilbert space theory, which was cast in terms of quadratic forms in infinitely many variables. The original spectral theorem was therefore conceived as a version of the theorem on principal axes of an ellipsoid , in an infinite-dimensional setting.
The Laplacian matrix is the easiest to define for a simple graph but more common in applications for an edge-weighted graph, i.e., with weights on its edges — the entries of the graph adjacency matrix. Spectral graph theory relates properties of a graph to a spectrum, i.e., eigenvalues and eigenvectors of matrices associated with the graph ...
In mathematics, spectral theory deals with attempts to understand operators, graphs and dynamical systems by means of the spectrum of eigenvalues associated with the system. The classical examples of spectra are the vibration modes of a violin string or the spectrum of a hydrogen atom .