Large language model (LLM)-based multi-agent systems have shown strong capabilities in tasks such as code generation and collaborative reasoning. However, the effectiveness and robustness of these systems critically depend on their communication topology, which is often fixed or statically learned, ignoring real-world dynamics such as model upgrades, API (or tool) changes, or knowledge source variability. To address this limitation, we propose CARD (Conditional Agentic Graph Designer), a conditional graph-generation framework that instantiates AMACP, a protocol for adaptive multi-agent communication. CARD explicitly incorporates dynamic environmental signals into graph construction, enabling topology adaptation at both training and runtime. Through a conditional variational graph encoder and environment-aware optimization, CARD produces communication structures that are both effective and resilient to shifts in model capability or resource availability. Empirical results on HumanEval, MATH, and MMLU demonstrate that CARD consistently outperforms static and prompt-based baselines, achieving higher accuracy and robustness across diverse conditions. The source code is available at: https://github.com/Warma10032/CARD.