History
The Cayley Graph was first considered for finite groups by Cayley in 1878. Max Dehn in his unpublished lectures on group theory from 1909-10 reintroduced Cayley graphs under the name Gruppenbild (group diagram), which led to the geometric group theory of today. His most important application was the solution of the word problem for the fundamental group of surfaces with genus ≥ 2, which is equivalent to the topological problem of deciding which closed curves on the surface contract to a point.
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