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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 ...
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 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 ...
Erdős on Graphs: His Legacy of Unsolved Problems is a book on unsolved problems in mathematics collected by Paul Erdős in the area of graph theory. It was written by Fan Chung and Ronald Graham, based on a 1997 survey paper by Chung, [1] and published in 1998 by A K Peters. A softcover edition with some updates and corrections followed in 1999.
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;
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.
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.
The expander mixing lemma intuitively states that the edges of certain -regular graphs are evenly distributed throughout the graph. In particular, the number of edges between two vertex subsets S {\displaystyle S} and T {\displaystyle T} is always close to the expected number of edges between them in a random d {\displaystyle d} - regular graph ...