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Discrete mathematics
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===Graph theory=== {{Main|Graph theory}} [[File:TruncatedTetrahedron.gif|thumb|right|200px|[[Graph theory]] has close links to [[group theory]]. This [[truncated tetrahedron]] graph is related to the [[alternating group]] ''A''<sub>4</sub>.]] Graph theory, the study of [[Graph (discrete mathematics)|graphs]] and [[network theory|networks]], is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right.<ref>{{cite book |author1-link=Bojan Mohar |author2-link=Carsten Thomassen (mathematician) |first1=Bojan |last1=Mohar |first2=Carsten |last2=Thomassen |title=Graphs on Surfaces |publisher=Johns Hopkins University Press |date=2001 |isbn=978-0-8018-6689-0 |oclc=45102952 |url=https://www.press.jhu.edu/books/title/1675/graphs-surfaces }}</ref> Graphs are one of the prime objects of study in discrete mathematics. They are among the most ubiquitous models of both natural and human-made structures. They can model many types of relations and process dynamics in physical, biological and social systems. In computer science, they can represent networks of communication, data organization, computational devices, the flow of computation, etc. In mathematics, they are useful in geometry and certain parts of [[topology]], e.g. [[knot theory]]. [[Algebraic graph theory]] has close links with group theory and [[topological graph theory]] has close links to [[topology]]. There are also [[continuous graph]]s; however, for the most part, research in graph theory falls within the domain of discrete mathematics.
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