Commit messages explain code changes in a commit and facilitate collaboration among developers. Several commit message generation approaches have been proposed; however, they exhibit limited success in capturing the context of code changes. We propose Comet (Context-Aware Commit Message Generation), a novel approach that captures context of code changes using a graph-based representation and leverages a transformer-based model to generate high-quality commit messages. Our proposed method utilizes delta graph that we developed to effectively represent code differences. We also introduce a customizable quality assurance module to identify optimal messages, mitigating subjectivity in commit messages. Experiments show that Comet outperforms state-of-the-art techniques in terms of bleu-norm and meteor metrics while being comparable in terms of rogue-l. Additionally, we compare the proposed approach with the popular gpt-3.5-turbo model, along with gpt-4-turbo; the most capable GPT model, over zero-shot, one-shot, and multi-shot settings. We found Comet outperforming the GPT models, on five and four metrics respectively and provide competitive results with the two other metrics. The study has implications for researchers, tool developers, and software developers. Software developers may utilize Comet to generate context-aware commit messages. Researchers and tool developers can apply the proposed delta graph technique in similar contexts, like code review summarization.