Various Labelling for Double Star Graph

In this work, we introduce labeling techniques for the double star graph, a basic graph theory structure. In particular, we concentrate on calculating two different kinds of labeling: fortunate labeling and correct labeling. Adhering to the restrictions of vertex labeling in graph theory, appropriate labeling guarantees that neighboring vertices receive unique labels. A more recent and interesting idea is the fortunate labelling, which gives vertices positive numbers so that the labels on neighboring vertices add up to a unique value for each edge. We calculate and examine various labeling methods using algorithmic methods, proving their usefulness and effectiveness for the double star graph. Our findings further enhance the theoretical and practical capabilities of various labeling systems by offering insightful information about how to optimize them for bipartite and tree-like graphs.