The Cayley Property of Some Distant Graphs and Relationship with the Stern-Brocot Tree

摘要

One of the graphs associated with any ring R is its distant graph G(R, Delta) with points of the projective line P(R) over R as vertices. We prove that the distant graph of any commutative, Artinian ring is a Cayley graph. The main result is the fact that G(Z, Delta) is a Cayley graph of a non-artinian commutative ring. We indicate two non-isomorphic subgroups of PSL2(Z) corresponding to this graph.