Existing computation and communication (2C) optimization schemes for cellular-based vehicle-to-everything (C-V2X) networks do not consider the influence of social trust. Computational tasks may be offloaded to untrusted vehicles, hindering the accurate execution of computational tasks. This may lead to a re-offloading of the computational tasks, consuming additional power, and decreasing the energy efficiency (EE) for offloading. To address this issue, this work devotes itself to investigating the social-mobility-aware underlying C-V2X framework and proposes a novel EE-oriented 2C assignment scheme. In doing so, we assume that the task vehicular user (T-VU) can offload computational tasks to the service vehicular user (S-VU) and the road side unit (RSU). In Sect. 5.2, an EE maximization problem to assign 2C resources simultaneously through joint optimization is formulated, which is a mixed-integer nonlinear programming (MINLP) problem. To solve this problem, we transform it into separate computation and communication resource allocation subproblems in Sect. 5.3. To address the first subproblem, we fully integrate the social and mobility characteristics and design a heuristic algorithm to achieve edge server selection and task splitting. To address the complex co-channel interference in the second subproblem, the power allocation and spectrum assignment solutions are obtained via a tightening lower bound method and a Kuhn-Munkres (KM) algorithm. Finally, we solve the original problem through an iterative method. In Sect. 5.4, the simulation results show that the proposed scheme can significantly enhance the system EE. Section 5.5 concludes the work.