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A bipartite graph G with partite sets X and Y is called consecutively super edge-magic if there exists a bijective function f : V ( G ) ⋃ E ( G ) → {1,2,...,| V ( G )| + | E ( G )|} with the property that f ( X ) = {1,2,...,| X |}, f ( Y ) = {| X |+1, | X |+2,...,| V ( G )|} and f ( u )+ f ( v ) + f ( uv ) is constant for each uv ∈ E ( G ). The question studied in this paper is for which bipartite graphs it is possible to add a finite number of isolated vertices so that the resulting graph is consecutively super edge-magic. If it is possible for a bipartite graph G , then we say that the minimum such number of isolated vertices is the consecutively super edge-magic deficiency of G ; otherwise, we define it to be +∞. This paper also includes a detailed discussion of other concepts that are closely related to the consecutively super edge-magic deficiency.

The consecutively super edge-magic deficiency of graphs and related concepts