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With the development of wireless communications and the intellectualization of machines, the Internet of Things (IoT) has been of interest to both industry and academia. Multihop routing and relaying are key technologies that will underpin IoT mesh networks in the future. This paper investigates optimal routing based on the trusted connectivity probability (T-CP) for multihop, underlay, device-to-device (D2D) communications with decode-and-forward relaying. Both random and fixed locations for base stations (BSs) are considered, where the former case assumes that the locations of the BSs are modeled as a Poisson point process (PPP). First, we derive two expressions for the connectivity probability (CP): 1) a tight lower bound and 2) an exact closed-form. Analysis is carried out for the cases where the channel state information (CSI) between BSs and the D2D transmitter is known (CSI-aware) and unknown (noCSI …