  We exactly evaluate a number of multipartite entanglement measures for a
class of graph states, including d-dimensional cluster states (d = 1,2,3), the
Greenberger-Horne-Zeilinger states, and some related mixed states. The
entanglement measures that we consider are continuous, `distance from separable
states' measures, including the relative entropy, the so-called geometric
measure, and robustness of entanglement. We also show that for our class of
graph states these entanglement values give an operational interpretation as
the maximal number of graph states distinguishable by local operations and
classical communication (LOCC), as well as supplying a tight bound on the fixed
letter classical capacity under LOCC decoding.
