  In this work we address the realizability of a Lyapunov graph labeled with GS
singularities, namely regular, cone, Whitney, double crossing and triple
crossing singularities, as continuous flow on a singular closed $2$-manifold
$\mathbf{M}$. Furthermore, the Euler characteristic is computed with respect to
the types of GS singularities of the flow on $\mathbf{M}$. Locally, a complete
classification theorem for minimal isolating blocks of GS singularities is
presented in terms of the branched one manifolds that make up the boundary.
