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Autonomous vehicles offer various advantages to both vehicle owners and automobile companies. However, despite the advantages, there are various risks associated with these vehicles. These vehicles interact with each other by forming a vehicular network, also known as VANET, in a centralized manner. This centralized network is vulnerable to cyber-attacks which can cause data loss, resulting in road accidents. Thus, to prevent the vehicular network from being attacked and to prevent the privacy of the data, key management is used. However, key management alone over a centralized network is not effective in ensuring data integrity in a vehicular network. To resolve this issue, various studies have introduced a blockchain-based approach and enabled key management over a decentralized network. This technique is also found effective in ensuring the privacy of all the stakeholders involved in a vehicular network. Furthermore, a blockchain-based key management system can also help in storing a large amount of data over a distributed network, which can encourage a faster exchange of information between vehicles in a network. However, there are certain limitations of blockchain technology that may affect the efficient working of autonomous vehicles. Most of the existing blockchain-based systems are implemented over Ethereum or Bitcoin. The transaction-processing capability of these blockchains is in the range of 5 to 20 transactions per second, whereas hashgraphs are capable of processing thousands of transactions per second as the data are processed exponentially. Furthermore, a hashgraph prevents the user from altering the order of the transactions being processed, and they do not need high computational powers to operate, which may help in reducing the overall cost of the system. Due to the advantages offered by a hashgraph, an advanced key management framework based on a hashgraph for secure communication between the vehicles is suggested in this paper. The framework is developed using the concept of Leaving of Vehicles based on a Logical Key Hierarchy (LKH) and Batch Rekeying. The system is tested and compared with other closely related systems on the basis of the transaction compilation time and change in traffic rates. [ABSTRACT FROM AUTHOR]