Sequential diagnosis requires balancing diagnostic accuracy against resource costs through iterative information gathering. Existing Large Language Model (LLM) approaches exhibit a critical knowledge-reasoning gap: despite encoding extensive medical knowledge, they struggle to reason systematically under cost constraints, often resorting to excessive testing. We propose GraphDx, a knowledge-enhanced framework with two core innovations. First, we design an automated pipeline that leverages LLMs to construct Medical Diagnosis Knowledge Graphs (MDKGs) with quantized typicality, action-centric topology, and dual-objective attributes for both diagnostic relevance and cost-sensitivity. Second, we introduce three collaborative agents (Perception, Reasoning, and Decision) where the Perception and Decision Agents handle language understanding and generation, while the Reasoning Agent performs deterministic evidence scoring and cost-aware planning on the MDKG. Experiments on MedQA and MIMIC-IV across three LLM backbones (DeepSeek-V3, Kimi-k2, Llama-3.3) show that GraphDx improves diagnostic success rates from 50–68% to 79–93% while reducing test costs by 20–54%, providing a robust, economical, and interpretable solution for automated clinical diagnosis.