Localization of mobile systems with visual Simultaneous Localization and Mapping (SLAM) is computationally expensive and therefore leads to high power consumption. The higher power consumption results in a shorter runtime for battery-powered mobile systems. A feasible solution to save energy for mobile systems is to offload SLAM to an external server. To achieve low latencies this server should be in close proximity to the mobile system at the edge. We evaluate the energy savings for three different offloading schemes for visual SLAM: (i) local computation on the mobile system, (ii) partially offloaded, and (iii) fully offloaded. We demonstrate that the power consumption can be reduced by up to 43 % by fully offloading the computation of visual SLAM. Furthermore, for the partially offloading scheme, the power consumption can be reduced by more than 20 % with the advantage of requiring a lower bit rate to transmit the sensor data compared to the fully offloaded scheme. Our paper shows the trade-off between power consumption and network utilization for offloading visual SLAM.