<![CDATA[This study focuses on the significant branch of graph theory known as graceful labeling, which involves assigning integers to the vertices and edges of graphs. Various techniques, such as vertex-graceful, edge-graceful, harmonious, lucky, magic, and prime labeling, have been developed to address this problem. Despite the extensive research on graceful labeling, the specific challenge of labeling pendant graphs gracefully has not been widely explored. Our research proposes new algorithms for gracefully labeling graphs with pendant vertices. These algorithms can be applied to various types of graphs, including cyclic, tetrahedron, regular, octahedron, complete, and square pyramid graphs. By introducing these new methods, we aim to fill the gap in the literature regarding pendant graphs. The study concludes with a detailed case study that illustrates the practical application of the proposed algorithms, demonstrating their effectiveness and ease of use in gracefully labeling pendant graphs. This contribution provides a valuable addition to the existing body of knowledge on graph labeling]]>
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