  In this paper, we consider the inverse dynamic problem for the Dirac system
on finite metric tree graphs. Our main goal is to recover the topology
(connectivity) of a tree, lengths of edges, and a matrix potential function on
each edge. We use the dynamic response operator as our inverse data and apply
the Leaf peeling method. In addition, we present a new dynamic algorithm to
solve the forward problem for the Dirac system on general finite metric graphs.
