On nearly distance magic graphs
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2017
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International Conference, ICTCSDM 2016, Krishnankoil, India, December 19-21, 2016
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.
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Godinho, A., Singh, T., & Arumugam, S. (2017). On nearly distance magic graphs. In Theoretical Computer Science and Discrete Mathematics: First International Conference, ICTCSDM 2016, Krishnankoil, India, December 19-21, 2016, Revised Selected Papers 1 (pp. 76-82). Springer International Publishing.