  Connected and automated vehicles have shown great potential in improving
traffic mobility and reducing emissions, especially at unsignalized
intersections. Previous research has shown that vehicle passing order is the
key influencing factor in improving intersection traffic mobility. In this
paper, we propose a graph-based cooperation method to formalize the
conflict-free scheduling problem at an unsignalized intersection. Based on
graphical analysis, a vehicle's trajectory conflict relationship is modeled as
a conflict directed graph and a coexisting undirected graph. Then, two
graph-based methods are proposed to find the vehicle passing order. The first
is an improved depth-first spanning tree algorithm, which aims to find the
local optimal passing order vehicle by vehicle. The other novel method is a
minimum clique cover algorithm, which identifies the global optimal solution.
Finally, a distributed control framework and communication topology are
presented to realize the conflict-free cooperation of vehicles. Extensive
numerical simulations are conducted for various numbers of vehicles and traffic
volumes, and the simulation results prove the effectiveness of the proposed
algorithms.
