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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.
Visualization comparing the sheet and the binary tree Cayley graph of (,). Red and blue edges correspond to a {\displaystyle a} and b {\displaystyle b} , respectively. In the mathematical field of group theory , the Baumslag–Solitar groups are examples of two-generator one-relator groups that play an important role in combinatorial group ...
This is usually done by studying the Cayley graphs of groups, which, in addition to the graph structure, are endowed with the structure of a metric space, given by the so-called word metric. Geometric group theory, as a distinct area, is relatively new, and became a clearly identifiable branch of mathematics in the late 1980s and early 1990s.
The same file with right action (which is more usual for Cayley graphs). One of the Cayley graphs of the dihedral group Dih 4. This version of File:Dih 4 Cayley Graph; generators a, b.svg uses prefix notation, which is unusual for Cayley graphs. In this file an arrow for s goes from g to sg, while in the other file it goes from g to gs.
Description: Cayley table of Dih 4 (right action). One of the Cayley graphs of the dihedral group Dih 4. The red arrow represents permutation =, and the blue edge represents permutation =.
Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Help. Pages in category "Cayley graphs" The following 3 pages are in this ...
The Hamiltonian cycle in the Cayley graph of the symmetric group generated by the Steinhaus–Johnson–Trotter algorithm Wheel diagram of all permutations of length = generated by the Steinhaus-Johnson-Trotter algorithm, where each permutation is color-coded (1=blue, 2=green, 3=yellow, 4=red).
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