  Let a and b be positive, relatively prime integers. We show that the
following are equivalent: (i) d is a dead end in the (symmetric) Cayley graph
of Z with respect to a and b, (ii) d is a Frobenius value with respect to a and
b (it cannot be written as a non-negative or non-positive integer linear
combination of a and b), and d is maximal (in the Cayley graph) with respect to
this property. In addition, for given integers a and b, we explicitly describe
all such elements in Z. Finally, we show that Z has only finitely many dead
ends with respect to any finite symmetric generating set. In the appendix we
show that every finitely generated group has a generating set with respect to
which dead ends exist.
