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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 ...
For every graph G, there exists a highly irregular graph H containing G as an induced subgraph. [ 3 ] This last observation can be considered analogous to a result of Dénes Kőnig , which states that if H is a graph with greatest degree r , then there is a graph G which is r -regular and contains H as an induced subgraph.
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 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 ...
This is a list of graph theory topics, by Wikipedia page. See glossary of graph theory for basic terminology. ... Spectral graph theory; Spring-based algorithm;
Spectral theory is connected with the investigation of localized vibrations of a variety of different objects, from atoms and molecules in chemistry to obstacles in acoustic waveguides. These vibrations have frequencies , and the issue is to decide when such localized vibrations occur, and how to go about computing the frequencies.
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.