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In order to ensure efficient data transmission from satellites to ground stations (GSs), resource allocation schemes must be designed. In cases where direct data transmission from satellites to GSs is not possible due to a dynamic network topology and limited contact time, efficient relay selection or route selection schemes should be employed. This paper considers a satellite communication network in which a number of source low earth orbit(SLEO) satellites are attempting to transmit their data flows to the designated GSs. To improve the transmission performance of the data flows, one geosynchronous earth orbit (GEO) satellite and a number of relay LEO (RLEO) satellites in the network are used as relays. To maximize energy efficiency, a joint route selection and resource allocation mechanism is proposed. The energy cost of the system, which is the sum of the energy cost of the SLEO satellites and the RLEO satellites, is used to formulate the joint route selection and resource allocation as a system energy cost minimization problem. Since the original optimization problem is NP hard, it is transformed into three subproblems: inter-satellite power allocation, satellite-ground power allocation, and route selection. These subproblems are solved using a greedy algorithm, the Lagrange dual method, and a matching-based heuristic algorithm, respectively. The numerical results demonstrate the effectiveness of the proposed scheme.