Editing Cayley graph (section)

{{Short description|Graph defined from a mathematical group}}
[[Image:Cayley graph of F2.svg|right|thumb|The Cayley graph of the [[free group]] on two generators ''a'' and ''b'']]
{{Graph families defined by their automorphisms}}
In [[mathematics]], a '''Cayley graph''', also known as a '''Cayley color graph''', '''Cayley diagram''', '''group diagram''', or '''color group''',<ref name = CGT>{{cite book |author-link=Wilhelm Magnus |first1=Wilhelm |last1=Magnus |first2=Abraham |last2=Karrass |author3-link=Baumslag–Solitar group |first3=Donald |last3=Solitar |title=Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations |url=https://books.google.com/books?id=1LW4s1RDRHQC&pg=PR2 |year=2004 |orig-year=1966 |publisher=Courier |isbn=978-0-486-43830-6 }}</ref> is a [[Graph (discrete mathematics)|graph]] that encodes the abstract structure of a [[group (mathematics)|group]]. Its definition is suggested by [[Cayley's theorem]] (named after [[Arthur Cayley]]), and uses a specified [[generating set of a group|set of generators]] for the group. It is a central tool in [[combinatorial group theory|combinatorial]] and [[geometric group theory]]. The structure and symmetry of Cayley graphs make them particularly good candidates for constructing [[expander graphs]].