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Introduced by Rosa in 1967, graceful labeling has been widely studied, and the Graceful Tree Conjecture asserts that every tree is graceful. The conjecture is known to hold for several classes of trees, including caterpillars, trees with at most four leaves, trees of diameter at most five, and certain spiders. 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If such a labeling exists, then we call $G$ \\emph{graceful}. Introduced by Rosa in 1967, graceful labeling has been widely studied, and the Graceful Tree Conjecture asserts that every tree is graceful. The conjecture is known to hold for several classes of trees, including caterpillars, trees with at most four leaves, trees of diameter at most five, and certain spiders. 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