  We count the ordered sum-free triplets of subsets in the group
$\mathbb{Z}/p\mathbb{Z}$, i.e., the triplets $(A,B,C)$ of sets $A,B,C \subset
\mathbb{Z}/p\mathbb{Z}$ for which the equation $a+b=c$ has no solution with
$a\in A$, $b \in B$ and $c \in C$. Our main theorem improves on a recent result
by Semchankau, Shabanov, and Shkredov using a different and simpler method. Our
proof relates previous results on the number of independent sets of regular
graphs by Kahn, Perarnau and Perkins, and Csikv\'ari to produce explicit
estimates on smaller order terms. We also obtain estimates for the number of
sum-free triplets of subsets in a general abelian group.
