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Let G=(V,E) be a finite simple graph with p vertices and q edges, without isolated vertices or isolated edges. A vertex magic total labeling is a bijection f from V∪E to the consecutive integers 1,2,⋯,p+q, with the property that, for every vertex u∈V, one has f(u)+∑uv∈Ef(uv)=k for some constant k. The vertex magic total labeling is called E-super if f(E)={1,2,⋯,q}. In this paper we verify the existence...
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