Autonomous driving is a promising technology to reduce traffic accidents and improve driving efficiency. In this work, a deep reinforcement learning (DRL)-enabled decision-making policy is constructed for autonomous vehicles to address the overtaking behaviors on the highway. First, a highway driving environment is founded, wherein the ego vehicle aims to pass through the surrounding vehicles with an efficient and safe maneuver. A hierarchical control framework is presented to control these vehicles, which indicates the upper-level manages the driving decisions, and the lower-level cares about the supervision of vehicle speed and acceleration. Then, the particular DRL method named dueling deep Qnetwork (DDQN) algorithm is applied to derive the highway decision-making strategy. The exhaustive calculative procedures of deep Q-network and DDQN algorithms are discussed and compared. Finally, a series of estimation simulation experiments are conducted to evaluate the effectiveness of the proposed highway decision-making policy. The advantages of the proposed framework in convergence rate and control performance are illuminated. Simulation results reveal that the DDQN-based overtaking policy could accomplish highway driving tasks efficiently and safely. INDEX TERMS Autonomous driving, decision-making, deep reinforcement learning, dueling deep Qnetwork, deep Q-learning, overtaking policy.

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A graph G is said to be F-residual if for every point u in G, the graph obtained by removing the closed neighborhood of u from G is isomorphic to F. Similarly, if the remove of m consecutive closed neighborhoods yields Kn, then G is called m-Kn-residual graph. Erdös determine the minimum order of the m-Kn-residual graph for all m and n, the minimum order of the connected Kn-residual graph is found and all the extremal graphs are specified. Jiangdong Liao and Shihui Yang determine the minimum order of the connected 2-Kn-residual graph is found and all the extremal graphs are specified expected for n=3, and in this paper, we prove that the minimum order of the connected 3-Kn-residual graph is found and all the extremal graphs are specified expected for n=5, 7, 9,10, and we revised Erdös conjecture.