In cellular vehicle-to-everything systems, the rapid movement of vehicles leads to the network topology instability of device-to-device (D2D) links. The frequent reconfiguration of network topology increases the complexity of the same frequency interference problem and the amount of signaling overhead for the management of network topology, which result in the waste of the computation ability and bandwidth resources of the base station (BS). In this paper, we establish a full-duplex device-to-device (FD-D2D) vehicular communication model with cluster as the core and propose a resource management scheme for FD-D2D vehicular communication by using hypergraph clustering and interference limited area theory. In the proposed scheme, the degree of link dependence and the computation ability of vehicle users are utilized to improve the cluster survival time and reduce the BS overhead. Meanwhile, dynamic power control and sharing area mapping are used to assist the BS in allocating resources, reduce the co-frequency interference between vehicular device-to-device (V-D2D) links and between V-D2D links and cellular links that reuse the same frequency, and improve spectrum efficiency. Real-time traffic flow data are generated by the traffic simulation modeling software VISSIM to verify the proposed resource management scheme. Simulation results show that the network topology management workload of the BS is reduced by at least 50%. Relative to that in traditional cellular D2D vehicle communication, the average frequency of spectrum sharing in FD-D2D communication increases by more than 0.5 times, and the spectrum efficiency increases by 10%.