  Identifying and locating-dominating codes have been widely studied in
circulant graphs of type $C_n(1,2, \ldots, r)$, which can also be viewed as
power graphs of cycles. Recently, Ghebleh and Niepel (2013) considered
identification and location-domination in the circulant graphs $C_n(1,3)$. They
showed that the smallest cardinality of a locating-dominating code in
$C_n(1,3)$ is at least $\lceil n/3 \rceil$ and at most $\lceil n/3 \rceil + 1$
for all $n \geq 9$. Moreover, they proved that the lower bound is strict when
$n \equiv 0, 1, 4 \pmod{6}$ and conjectured that the lower bound can be
increased by one for other $n$. In this paper, we prove their conjecture.
Similarly, they showed that the smallest cardinality of an identifying code in
$C_n(1,3)$ is at least $\lceil 4n/11 \rceil$ and at most $\lceil 4n/11 \rceil +
1$ for all $n \geq 11$. Furthermore, they proved that the lower bound is
attained for most of the lengths $n$ and conjectured that in the rest of the
cases the lower bound can improved by one. This conjecture is also proved in
the paper. The proofs of the conjectures are based on a novel approach which,
instead of making use of the local properties of the graphs as is usual to
identification and location-domination, also manages to take advantage of the
global properties of the codes and the underlying graphs.
