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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 ...
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.
Algebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants.
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 .
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory , design of robust computer networks , and the theory of error-correcting ...
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