Implementation of smart cities has brought a lot of comforts in our daily life. The smart cities are realized by using IT based services in the domain of transportation, health care, building management and so forth. In order to provide these services, vital information has to be sensed and disseminated using Internet-of-Things (IoT) devices, which are sparsely deployed in a smart city. These devices have low end processors and sometimes, they are installed in places where battery replacement is not feasible. In addition, they are also vulnerable to security attacks by the malicious nodes. There are a lot of recent attacks where IoT networks have been targeted by the hackers to launch a coordinated cyber attacks on some web domains. Therefore, there is a need to develop secure IoT solutions for smart cities that consume low energy. Due to its lightweight but powerful mechanisms, trust management is a promising technology to establish security for the heavily resource-constrained devices that are characteristic of the Internet of Things (IoT). In this paper, we develop an approach using trust management and investigate how it can be improved to work more energy-friendly. In particular, we adapt our mechanism to the IEEE 802.15.4 protocol. Further, we analyze the outcome of these adaptations finding out that they can reduce the active listening time of IoT nodes significantly.