Abstract
LetGbe a finite, simple, and undirected graph with vertex setVGand edge setEG. A super edge-magic labeling ofGis a bijectionf:VG∪EG⟶1,2,…,VG+EGsuch thatfVG=1,2,…,VGandfu+fuv+fvis a constant for every edgeuv∈EG. The super edge-magic labelingfofGis called consecutively super edge-magic ifGis a bipartite graph with partite setsAandBsuch thatfA=1,2,…,AandfB=A+1,A+2,…,VG. A graph that admits (consecutively) super edge-magic labeling is called a (consecutively) super edge-magic graph. The super edge-magic deficiency ofG, denoted byμsG, is either the minimum nonnegative integernsuch thatG∪nK1is super edge-magic or+∞if there exists no suchn. The consecutively super edge-magic deficiency of a graphGis defined by a similar way. In this paper, we investigate the (consecutively) super edge-magic deficiency of subdivision of double stars. We show that, some of them have zero (consecutively) super edge-magic deficiency.
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