This paper proposes a new auxiliary-graph-based green-lightpath provisioning algorithm for WDM networks that use optical regenerators. Energy efficiency in communication networks has become a critical issue recently since the total energy consumption of networks has been increasing year by year due to the growth of the Internet traffic. A lightpath introduces optical cut-through, which suppresses energy-inefficient IP packet processing at the intermediate nodes, and thus the total energy consumption of networks. An algorithm for dynamic lightpath establishment is a key factor in achieving high energy efficiency. When calculating a path, the energy consumption of optical regenerators, which are used at the intermediate nodes to guarantee optical signal quality, should be considered. To the best of our knowledge, however, the use of optical regenerators is not considered in previous studies on green-lightpath provisioning. The proposed auxiliary-graph-based algorithm can easily calculate the most energy efficient path considering the energy consumption of optical regenerators since the problem is transformed into the minimum weight path problem on the proposed auxiliary graph. Computer simulations show that our proposal reduces the blocking probability and the total energy consumption of a network.