  We study the spectrum of a self-adjoint Dirac-Krein operator with potential
on a compact star graph $\mathcal G$ with a finite number $n$ of edges. This
operator is defined by a Dirac-Krein differential expression with summable
matrix potentials on each edge, by self-adjoint boundary conditions at the
outer vertices, and by a self-adjoint matching condition at the common central
vertex of $\mathcal G$. Special attention is paid to Robin matching conditions
with parameter $\tau \in\mathbb R\cup\{\infty\}$. Choosing the decoupled
operator with Dirichlet condition at the central vertex as a reference
operator, we derive Krein's resolvent formula, introduce corresponding
Weyl-Titchmarsh functions, study the multiplicities, dependence on $\tau$, and
interlacing properties of the eigenvalues, and prove a trace formula. Moreover,
we show that, asymptotically for $R\to \infty$, the difference of the number of
eigenvalues in the intervals $[0,R)$ and $[-R,0)$ deviates from some integer
$\kappa_0$, which we call dislocation index, at most by $n+2$.
