  A nonnegative integer $p$ is realizable by a graph-theoretical invariant $I$
if there exist a graph $G$ such that $I(G) = p$. The inverse problem for $I$
consists of finding all nonnegative integers $p$ realizable by $I$. In this
paper, we consider and solve the inverse problem for the Mostar index, a
recently introduced graph-theoretical invariant which attracted a lot of
attention in recent years in both the mathematical and the chemical community.
We show that a nonnegative integer is realizable by the Mostar index if and
only if it is not equal to one. Besides presenting the complete solution to the
problem, we also present some empirical observations and outline several open
problems and possible directions for further research.
