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Complete Bipartite Graph
In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set..Electronic edition page 17. Graph theory itself is typically dated as beginning with Leonhard Euler's 1736 work on the Seven Bridges of Königsberg. However, drawings of complete bipartite graphs were already printed as early as 1669, in connection with an edition of the works of Ramon Llull edited by Athanasius Kircher. Llull himself had made similar drawings of complete graphs three centuries earlier.. Definition A complete bipartite graph is a graph whose vertices can be partitioned into two subsets and such that no edge has both endpoints in the same subset, and every possible edge that could connect vertices in different subsets is part of the graph. That is, it is a bipartite graph such that for every two vertices and, is an edge in . A complete bipartite graph with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claw (graph Theory)
In graph theory, a star is the complete bipartite graph a tree with one internal node and leaves (but no internal nodes and leaves when ). Alternatively, some authors define to be the tree of order with maximum diameter 2; in which case a star of has leaves. A star with 3 edges is called a claw. The star is edge-graceful when is even and not when is odd. It is an edge-transitive matchstick graph, and has diameter 2 (when ), girth ∞ (it has no cycles), chromatic index , and chromatic number 2 (when ). Additionally, the star has large automorphism group, namely, the symmetric group on letters. Stars may also be described as the only connected graphs in which at most one vertex has degree greater than one. Relation to other graph families Claws are notable in the definition of claw-free graphs, graphs that do not have any claw as an induced subgraph. They are also one of the exceptional cases of the Whitney graph isomorphism theorem: in general, graphs with isom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Complex Polygon
In geometry, a regular complex polygon is a generalization of a regular polygon in real coordinate space, real space to an analogous structure in a Complex number, complex Hilbert space, where each real dimension is accompanied by an imaginary number, imaginary one. A regular polygon exists in 2 real dimensions, \mathbb^2, while a complex polygon exists in two complex dimensions, \mathbb^2, which can be given real representations in 4 dimensions, \mathbb^4, which then must be projected down to 2 or 3 real dimensions to be visualized. A ''complex polygon'' is generalized as a complex polytope in \mathbb^n. A complex polygon may be understood as a collection of complex points, lines, planes, and so on, where every point is the junction of multiple lines, every line of multiple planes, and so on. The ''regular complex polygons'' have been completely characterized, and can be described using a symbolic notation developed by Harold Scott MacDonald Coxeter, Coxeter. A ''regular comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Polygon 2-4-5
Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each other * Complex (psychology), a core pattern of emotions etc. in the personal unconscious organized around a common theme such as power or status Complex may also refer to: Arts, entertainment and media * Complex (English band), formed in 1968, and their 1971 album ''Complex'' * Complex (band), a Japanese rock band * ''Complex'' (album), by Montaigne, 2019, and its title track * ''Complex'' (EP), by Rifle Sport, 1985 * "Complex" (song), by Gary Numan, 1979 * "Complex", a song by Katie Gregson-MacLeod, 2022 * "Complex" a song by Be'O and Zico, 2022 * Complex Networks, publisher of the now-only-online magazine ''Complex'' Biology * Protein–ligand complex, a complex of a protein bound with a ligand * Exosome complex, a multi-protei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomsen Graph
Thomsen is a Danish patronymic surname meaning 'son of Tom (or Thomas)', itself derived from the Aramaic תום or ''Tôm'', meaning "twin". There are many varied surname spellings, with the first historical record believed to be found in 1252. Thomsen is uncommon as a given name.Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 260. People with the surname Thomsen include: B * Britta Thomsen (born 1954), Danish politician and member of the European Parliament C * Cecilie Thomsen (born 1974), Danish actress and model * Christian Jürgensen Thomsen (1788–1865), Danish archaeologist * Claus Thomsen (born 1970), Danish former professional footballer E * Ebba Thomsen (1887–1973), Danish actress F * Finn Thomsen (born 1955), Danish motorcycle speedway rider * Fred Thomsen (1897–1986), American college football player and coach G * Gerhard Thomsen (1899–1934), German mathematician who worked in vari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Concept Analysis
In information science, formal concept analysis (FCA) is a principled way of deriving a ''concept hierarchy'' or formal ontology from a collection of objects and their properties. Each concept in the hierarchy represents the objects sharing some set of properties; and each sub-concept in the hierarchy represents a subset of the objects (as well as a superset of the properties) in the concepts above it. The term was introduced by Rudolf Wille in 1981, and builds on the mathematical theory of lattices and ordered sets that was developed by Garrett Birkhoff and others in the 1930s. Formal concept analysis finds practical application in fields including data mining, text mining, machine learning, knowledge management, semantic web, software development, chemistry and biology. Overview and history The original motivation of formal concept analysis was the search for real-world meaning of mathematical order theory. One such possibility of very general nature is that data tables ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heterogeneous Relation
In mathematics, a binary relation associates some elements of one set called the ''domain'' with some elements of another set called the ''codomain''. Precisely, a binary relation over sets X and Y is a set of ordered pairs (x, y), where x is an element of X and y is an element of Y. It encodes the common concept of relation: an element x is ''related'' to an element y, if and only if the pair (x, y) belongs to the set of ordered pairs that defines the binary relation. An example of a binary relation is the " divides" relation over the set of prime numbers \mathbb and the set of integers \mathbb, in which each prime p is related to each integer z that is a multiple of p, but not to an integer that is not a multiple of p. In this relation, for instance, the prime number 2 is related to numbers such as -4, 0, 6, 10, but not to 1 or 9, just as the prime number 3 is related to 0, 6, and 9, but not to 4 or 13. Binary relations, and especially homogeneous relations, are used in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
