  Graph tries are a new and interesting data structure proposed by Jacquet in
2014. They generalize the classical trie data structure which has found many
applications in computer science and is one of the most popular data structure
on words. For his generalization, Jacquet considered the size (or space
requirement) and derived an asymptotic expansion for the mean and the variance
when graph tries are built from $n$ independently chosen random labelings of a
rooted $M$-ary tree. Moreover, he conjectured a central limit theorem for the
(suitably normalized) size as the number of labelings tends to infinity. In
this paper, we verify this conjecture with the method of moments.
