In this article we propose a new paradigm of resource-efficient edge computing for the emerging intelligent IoT applications such as flying ad hoc networks for precision agriculture, e-health, and smart homes. We devise a resource-efficient edge computing scheme such that an intelligent IoT device user can well support its computationally intensive task by proper task offloading across the local device, nearby helper device, and the edge cloud in proximity. Different from existing studies for mobile computation offloading, we explore the novel perspective of resource efficiency and devise an efficient computation offloading mechanism consisting of a delay-aware task graph partition algorithm and an optimal virtual machine selection method in order to minimize an intelligent IoT device's edge resource occupancy and meanwhile satisfy its QoS requirement. Performance evaluation corroborates the effectiveness and superior performance of the proposed resource-efficient edge computing scheme.