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A graph that admits a super edge-magic total labeling is called a SEMT graph. In this paper, we study the structure of connected unicyclic SEMT graphs with magic constant 3 =   q p  . We also enumerate SEMT labelings with 3 =   q p  , for connected unicyclic graphs that contain a star of maximum size m, with 1 4     p m p

Super edge-magic total labelings of connected unicyclic (p,q) graphs with magic constant p + q + 3