Multi-access edge computing (MEC) networks face significant challenges in managing congestion and safeguarding personal privacy data on a massive scale. Integrating trust awareness into MEC networks presents an opportunity to enhance security and privacy by correlating human relationships with connected devices. Moreover, leveraging trust-aware task caching and offloading holds promise in mitigating latency and reducing energy consumption. Despite existing research efforts to address these challenges, they often overlook either trust awareness or caching optimization in task offloading, potentially compromising security or leading to task failures. To address this gap, this paper proposes a novel approach: a trust-aware task offloading strategy with cache constraints (TCTO) in MEC networks, which considers social relationships, task offloading, and caching. Drawing on the characteristics of bipartite graphs and bipartite perfect matching, we develop a trust-aware caching-constrained task offloading algorithm based on bipartite graphs. This algorithm aims to select task offloading strategies that minimize delay, energy consumption in task transmission and execution, while maximizing security among devices in MEC networks. Extensive simulations demonstrate that our proposed method has a better performance than other task offloading strategies for reducing delay and energy consumption in the process of task transmission and execution. Compared with the other baselines, the overhead of our proposed method is reduced
55
.
65
%
∼
96
.
20
%
compared with other baselines.