  We restrict geometric tangential equivariant complex $T^n$-bordism to torus
manifolds and provide a complete combinatorial description of the appropriate
non-commutative ring. We discover, using equivariant $K$-theory characteristic
numbers, that the information encoded in the oriented torus graph associated to
a stably complex torus manifold completely describes its equivariant bordism
class. We also consider the role of omnioriented quasitoric manifolds in this
description.
