Symbolic execution is a critical technique for detecting vulnerabilities in smart contracts on the blockchain. Existing tools struggle with high false positive rates and often fail to identify multi-function trigger vulnerabilities. To address these challenges, we introduce SVD-SESDG, which constructs a dependency graph for smart contract state variables to identify and analyze critical paths linked to potential vulnerabilities. By focusing on these paths and using actual state values to solve path constraints, SVD-SESDG enhances both efficiency and detection of complex vulnerabilities. Our experiments on an open-source dataset, targeting four types of vulnerabilities, demonstrate that SVD-SESDG significantly outperforms existing tools (Oyente, Mythril, TeEther) in reducing false positives and improving accuracy.