While backscatter communication emerges as a promising solution to reduce power consumption at IoT devices, the transmission range of backscatter communication is short. To this end, this work integrates unmanned ground vehicles (UGVs) into the backscatter system. With such a scheme, the UGV could facilitate the communication by approaching various IoT devices. However, moving also costs energy consumption and a fundamental question is: what is the right balance between spending energy on moving versus on communication? To answer this question, this paper proposes a joint graph mobility and backscatter communication model. With the proposed model, the total energy minimization at UGV is formulated as a mixed integer nonlinear programming (MINLP) problem. Furthermore, an efficient algorithm that achieves a local optimal solution is derived, and it leads to automatic trade-off between spending energy on moving versus on communication. Numerical results are provided to validate the performance of the proposed algorithm.