The augmented cube $A{Q}_n$ is a variation of the hypercube $Q_n$ . This paper considers the fault-tolerant Panconnectivity of $A{Q}_n$ . Assume that $F\subseteq V(A{Q}_n)\cup E(A{Q}_n)$ and $n\ge 4$ . We prove that for any two fault-free vertices $u$ and $v$ with distance $d$ in $A{Q}_n$ , there exists a fault-free path $P_{uv}$ of each length from $max\{d+2,4\}$ to $2^n-f_v-1$ in $A{Q}_n-F$ if $\left|F\right|\le 2n-4$ , where $f_v$ is the number of faulty vertices in $A{Q}_n$ . Moreover, the bound is sharp.

In order to improve the accuracy of vehicle trajectories and ensure driving safety, and considering the differences in driver behavior and the impact of these differences on vehicle trajectories, a vehicle trajectory-prediction method (DBC-Informer) based on the categorization of driver behavior is proposed: firstly, the characteristic driver feature data are extracted through data preprocessing; secondly, descriptive statistical data are obtained through the classification of the driver’s behavior into categories; finally, based on the Informer model, a two-layer driver category trajectory-prediction network architecture is established, which inputs the vehicle trajectories of different driving types into independent prediction sub-networks, respectively, to realize the accurate prediction of vehicle trajectories. The experimental results show that the MAE and MSE values of trajectory prediction of the DBC-Informer model in different time domains are much smaller than those of other comparative models, and the improvement of accuracy is more obvious in the long-term domain trajectory-prediction task scenario, and the increase in prediction error of the DBC-Informer model is significantly reduced after the prediction time exceeds 1 s. The on-line behavioral categorization is achieved by comparing different categorization models; it reaches 98% in classification accuracy and, according to the results of ablation experiments, the addition of the driver behavior-classification method to the prediction model improves the accuracy of prediction in longitudinal and lateral motion by 56% and 61%, respectively, which verifies the effectiveness of the driver behavior-classification method. It can be seen that the DBC-Informer model can more accurately portray the effects of different driving behaviors on vehicle trajectories and improve the accuracy of vehicle trajectory prediction, which provides important data support for vehicle warning systems.