  A smooth GKM stack is a smooth Deligne-Mumford stack equipped with an action
of an algebraic torus $T$, with only finitely many zero-dimensional and
one-dimensional orbits. (i) We define the stacky GKM graph of a smooth GKM
stack, under the mild assumption that any one-dimensional $T$-orbit closure
contains at least one $T$ fixed point. The stacky GKM graph is a decorated
graph which contains enough information to reconstruct the $T$-equivariant
formal neighborhood of the 1-skeleton (union of zero-dimensional and
one-dimensional $T$-orbits) as a formal smooth DM stack equipped with a
$T$-action. (ii) We axiomize the definition of a stacky GKM graph and introduce
abstract stacky GKM graphs which are more general than stacky GKM graphs of
honest smooth GKM stacks. From an abstract GKM graph we construct a formal
smooth GKM stack. (iii) We define equivariant orbifold Gromov-Witten invariants
of smooth GKM stacks, as well as formal equivariant orbifold Gromov-Witten
invariants of formal smooth GKM stacks. These invariants can be computed by
virtual localization and depend only the stacky GKM graph or the abstract
stacky GKM graph. Formal equivariant orbifold Gromov-Witten invariants of the
stacky GKM graph of a smooth GKM stack $\mathcal{X}$ are refinements of
equivariant orbifold Gromov-Witten invariants of $\mathcal{X}$.
