  In this paper we study the generation of Bell states between distant vertices
in a permanently coupled quantum spin network, interacting via invariant
stratification graphs. To begin with we establish a class of upper bounds over
achievable entanglement between the reference site and various vertices. We
observe that the maximum of these upper bounds is 1 e-bit. We conclude that the
reference site can generate a Bell state with a vertex if the corresponding
upper bound of the vertex is 1 e-bit. Thus for generation of a Bell state this
upper bound must be saturated. Taking this into account, we obtain the
characteristic constraint of the proper graphs. We introduce a special class of
antipodal invariant stratification graphs, which is called reflective, whereas
the antipode vertex obeys the characteristic constraint. We also show that the
antipodal association scheme graphs are reflective so Bell states can be
generated between the antipodal vertices. Moreover we observe that in such
graphs the proper Hamiltonian that enables creation of Bell state is the
Heisenberg interaction between vertex pairs.
