  We introduce a class of labeled graphs (with legs) which contains two classes
of GKM graphs of $4n$-dimensional manifolds with $T^{n}\times S^{1}$-actions,
i.e., GKM graphs of the toric hyperK${\rm\ddot{a}}$hler manifolds and of the
cotangent bundles of toric manifolds. Under some conditions, the graph
equivariant cohomology ring of such a labeled graph is computed. We also give a
module basis of the graph equivariant cohomology by using a shelling structure
of such a labeled graph and study their multiplicative structure.
