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A number of techniques have been proposed to provide adversarial robustness guarantees, but support for commonly used aggregation functions in message-passing GNNs is lacking. In this paper, we develop an exact (sound and complete) verification method for GNNs to compute guarantees against attribute and structural perturbations that involve edge addition or deletion, subject to budget constraints. Our method employs constraint solving with bound tightening, and iteratively solves a sequence of relaxed constraint satisfaction problems while relying on incremental solving capabilities of solvers to improve efficiency. 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