Title: Certified Robustness on Structural Graph Matching. Abstract: The vulnerability of graph matching (GM) to adversarial attacks has received increasing attention from emerging empirical studies, while the certified robustness of GM has not been explored. Motivated by randomized smoothing, we are the first to define certified robustness on GM and design a new certification strategy called Structure-based Certified Robustness of Graph Matching (SCR-GM). Structural prior information of nodes is used to construct a joint smoothing distribution matrix with physical significance, which certifies a wider range than those obtained by previous iterative optimization methods. Furthermore, we propose a certified space that can be used to derive a strictly certified radius and two radii for evaluation. Experimental results on graph matching datasets reveal that our strategy achieves state-of-the-art $\ell_{2}$ certified accuracy and regions.