Forest with two components 2-regular graph Join product graph A graph is called super edge-magic if there exists a bijection ∶ () ∪ () ⟶ {1, 2, ⋯ , | ()| + | ()|}, where (()) = {1, 2, ⋯ , | ()|}, such that () + () + () is a constant for every edge ∈ (). Such a case, is called a super edge magic labeling of. A bipartite graph with partite sets and is called consecutively super edge-magic if there exists a super edge-magic labeling with the property that () = {1, 2, ⋯ , | |} and () = {| | + 1, | | + 2, ⋯ , | ()|}. The super edge-magic deficiency of a graph , denoted by (), is either the minimum nonnegative integer such that ∪ 1 is super edge-magic or +∞ if there exists no such. The consecutively super edge-magic deficiency of a bipartite graph , denoted by (), is either the minimum nonnegative integer such that ∪ 1 is consecutively super edge-magic or +∞ if there exists no such. In this paper, we study the super edge-magic deficiency of some graphs. We investigate the (consecutively) super edge-magic deficiency of forests with two components. We also investigate the super edge-magic deficiency of a 2-regular graph 2 3 ∪ and join product of 1, ∪ with an isolated vertex.