Large language models (LLMs) have emerged as powerful tools for diverse NLP tasks, yet their deployment as autonomous multi-agent systems (MAS) for general problem-solving in the industry remains challenging. Current MAS frameworks often rely on manually designed and static collaboration graph structures, limiting adaptability and performance on different academic and industrial tasks. To address these limitations, we propose AdaSwarm, a dynamic framework that enhances LLM-based MAS through a key innovation: a dynamic graph selector that adaptively chooses the optimal graph structure for each input sample via parameter-efficient LLM fine-tuning. AdaSwarm eliminates the need for rigid, one-fits-all graph architectures, instead leveraging sample-specific idiosyncrasies to dynamically route queries through specialized agent networks. Extensive experiments on question answering, mathematical reasoning, and coding tasks demonstrate that AdaSwarm consistently outperforms state-of-the-art single-agent and MAS baselines across multiple LLM backbones. Our findings highlight the importance of sample-aware structural flexibility in LLM MAS designs.\footnote{Codes will be open-sourced to facilitate future research. }