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Electric, intelligent, and network are the most important future development directions of automobiles. Intelligent electric vehicles have shown great potentials to improve traffic mobility and reduce emissions, especially at unsignalized intersections. Previous research has shown that vehicle passing order is the key factor in traffic mobility improvement. In this paper, we propose a graph-based cooperation method to formalize the conflict-free scheduling problem at unsignalized intersections. Firstly, conflict directed graphs and coexisting undirected graphs are built to describe the conflict relationship of the vehicles. Then, two graph-based methods are introduced to solve the vehicle passing order. One method is an optimized depth - first spanning tree method which aims to find the local optimal passing order for each vehicle. The other method is a maximum matching algorithm that solves the global optimal problem …