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zero-symmetric. asymmetric. In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, [1] is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of generators for the group.
A Cayley graph is a graph defined from a pair (G,S) where G is a group and S is a set of generators for the group; it has a vertex for each group element, and an edge for each product of an element with a generator. In the case of a finite cyclic group, with its single generator, the Cayley graph is a cycle graph, and for an infinite cyclic ...
A Cayley graph of the symmetric group S 4 using the generators (red) a right circular shift of all four set elements, and (blue) a left circular shift of the first three set elements. Cayley table, with header omitted, of the symmetric group S 3. The elements are represented as matrices. To the left of the matrices, are their two-line form.
Cayley table. Named after the 19th century British mathematician Arthur Cayley, a Cayley table describes the structure of a finite group by arranging all the possible products of all the group's elements in a square table reminiscent of an addition or multiplication table. Many properties of a group – such as whether or not it is abelian ...
Presentation of a group. In mathematics, a presentation is one method of specifying a group. A presentation of a group G comprises a set S of generators —so that every element of the group can be written as a product of powers of some of these generators—and a set R of relations among those generators. We then say G has presentation.
Desmos was founded by Eli Luberoff, a math and physics double major from Yale University, [3] and was launched as a startup at TechCrunch 's Disrupt New York conference in 2011. [4] As of September 2012, it had received around 1 million US dollars of funding from Kapor Capital, Learn Capital, Kindler Capital, Elm Street Ventures and Google ...
In group theory, a subfield of abstract algebra, a cycle graph of a group is an undirected graph that illustrates the various cycles of that group, given a set of generators for the group. Cycle graphs are particularly useful in visualizing the structure of small finite groups . A cycle is the set of powers of a given group element a, where an ...
The Heawood graph is bipartite. In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and , that is, every edge connects a vertex in to one in . Vertex sets and are usually called the parts of the graph.
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