Smart city vision brings emerging heterogeneous communication technologies such as Fog Computing (FC) together to substantially reduce the latency and energy consumption of Internet of Everything (IoE) devices running various applications. The key feature that distinguishes the FC paradigm for smart cities is that it spreads communication and computing resources over the wired/wireless access network (e.g., proximate access points and base stations) to provide resource augmentation (e.g., cyberforaging) for resource and energy-limited wired/wireless (possibly mobile) things. Moreover, smart city applications are developed with the goal of improving the management of urban flows and allowing real-time responses to challenges that can arise in users' transactional relationships. This article presents a Fog-supported smart city network architecture called Fog Computing Architecture Network (FOCAN), a multi-tier structure in which the applications running on things jointly compute, route, and communicate with one another through the smart city environment to decrease latency and improve energy provisioning and the efficiency of services among things with different capabilities. An important concern that arises with the introduction of FOCAN is the need to avoid transferring data to/from distant things and instead to cover the nearest region for an IoT application. We define three types of communications between FOCAN devices (e.g., interprimary, primary, and secondary communication) to manage applications in a way that meets the quality of service standards for the IoE. One of the main advantages of FOCAN is that the devices can provide the services with low energy usage and in an efficient manner. Simulation results for a selected case study demonstrate the tremendous impact of the FOCAN energy-efficient solution on the communication performance of various types of things in smart cities.