Abstract
Power graphs of groups and semigroups constitute a significant class of graphs in algebraic graph theory, bridging algebraic structures and graph theoretic concepts. Further, labeling of graphs, particularly those endowed with an algebraic structure as their vertex set, is a vibrant area of research. This article contributes to this burgeoning field by exploring new classes of finite groups whose power graphs admit or forbid an important type of labeling called graceful labeling.
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