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A graph G is a sum graph if there exists a labeling of the vertices of G by distinct positive integers such that the vertices labeled u and v are adjacent if and only if there exists a vertex labeled u + v. The sum number σ(G) of a graph G is defined as the smallest number of isolated vertices which, when added to G results in a sum graph. A labeling that realizes G∪ σ(G)K 1 as a sum graph...
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