Internet of Things (IoT) employs a large number of sensors and actuators to collect and act upon data for its smart functionalities. These devices are considered as a part of the Low-power and Lossy Networks due to their use of low power embedded hardware and computationally constrained nature. For synchronization and utility, these devices are often clubbed together logically to form groups. To maintain data confidentiality within a group, a shared symmetric key called the Group Key (GK) is used by all the group members. The GK must be redistributed upon joining and leaving of a group member to maintain forward and backward secrecy. However, the key management (i.e., generation and distribution) process causes overhead which consumes the scarce network resources. In this paper, we propose TARE, a novel Topology Adaptive Re-kEying (TARE) scheme for lightweight and secure group communication. TARE integrates the principles of routing tree mapped logical key tree and local derivation of the key over the an IPv6 Routing Protocol for low-power and Lossy networks in an original way. TARE takes into consideration the current routing topology and makes maximum energy reduction as the premise for its choice of key derivation and distribution methods, thus, it reduces the network energy consumption while maintaining key secrecy and data confidentiality. In particular, TARE provides the following advantages: (1) lower network overhead and bandwidth utilization in key management and re-distribution operations, (2) effective against the network mobility in scalable IoT networks, (3) secure group communications in network against attacks such as man-in-the-middle and eavesdropping, and (4) data confidentiality by ensuring backward and forward secrecy in key distribution method. We evaluate the performance of TARE and compare it with existing schemes. Our results show the effectiveness of TARE regarding energy consumption, bandwidth utilization, and the number of encrypted message transmissions during the re-keying operations.