We consider the problem of learning a causal graph over a set of variables with interventions. We study the cost-optimal causal graph learning problem: For a given skeleton (undirected version of the causal graph), design the set of interventions with minimum total cost, that can uniquely identify any causal graph with the given skeleton. We show that this problem is solvable in polynomial time. Later, we consider the case when the number of interventions is limited. For this case, we provide polynomial time algorithms when the skeleton is a tree or a clique tree. For a general chordal skeleton, we develop an efficient greedy algorithm, which can be improved when the causal graph skeleton is an interval graph.