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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.
The Cayley graph of a free group with two generators. This is a hyperbolic group whose Gromov boundary is a Cantor set.Hyperbolic groups and their boundaries are important topics in geometric group theory, as are Cayley graphs.
Hence, the fundamental group of the Cayley graph Γ(G) is isomorphic to the kernel of φ, the normal subgroup of relations among the generators of G. The extreme case is when G = {e}, the trivial group, considered with as many generators as F, all of them trivial; the Cayley graph Γ(G) is a bouquet of circles, and its fundamental group is F ...
In mathematics, Cayley's formula is a result in graph theory named after Arthur Cayley. It states that for every positive integer n {\displaystyle n} , the number of trees on n {\displaystyle n} labeled vertices is n n − 2 {\displaystyle n^{n-2}} .
Download as PDF; Printable version; ... Free group; Modular groups. PSL(2, ... as shown by their Cayley and cycle graphs: Q 8 D 4; Cayley graph:
One sheet of the Cayley graph of the Baumslag–Solitar group BS(1, 2). Red edges correspond to a and blue edges correspond to b. The sheets of the Cayley graph of the Baumslag-Solitar group BS(1, 2) fit together into an infinite binary tree. Visualization comparing the sheet and the binary tree Cayley graph of (,).
Download as PDF; Printable version; In other projects ... Pages in category "Cayley graphs" The following 3 pages are in this category, out of 3 total. This ...
This is the corresponding graph, called the Nauru graph: The red, green and blue squares form the permutation matrices, indexed 1, 5 and 21 in the following file. (Compare: v:Symmetric_group_S4#A_closer_look_at_the_Cayley_table) 1, 5 and 21 are the generators of the Nauru graph. Source: Own work: Author