  We propose a mechanism to construct the eigenvalues and eigenfunctions of the
massless Dirac-Weyl equation in the presences of magnetic flux $\Phi$ localized
in a restricted region of the plane. Using this mechanism we analyze the
degeneracy of the existed energy levels. We find that the zero and first energy
level has the same $N+1$ degeneracy, where $N$ is the integer part of
$\frac{\Phi}{2\pi}$. In addition, and contrary to what is described in the
literature regarding graphene, we show that higher energy levels are $N+m$
degenrate, beign $m$ the level of energy. In other words, this implies an
indefinite growth of degenerate states as the energy level grows.
