On nearly distance magic graphs
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2017
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Abstract
Let G = (V, E) be a graph on n vertices. A bijection f ∶ V → {1, 2, . . . , n} is called a nearly distance magic labeling of G if there exist a positive integer k such that ∑x∈N(v) f(x) = k or k +1 for every v ∈ V . The constant k is called magic constants of the graph and the graph which admits such a labeling is called a nearly distance magic graph. In this paper we present several basic results on nearly distance magic graphs and compute the magic constant k in terms of the fractional total domination number of the graph.