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New Results on the (Super) Edge-Magic Deficiency of Chain Graphs

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  • Ngurah Anak Agung Gede
  • Adiwijaya

Abstract

Let be a graph of order and size . An edge-magic labeling of is a bijection such that is a constant for every edge . An edge-magic labeling of with is called a super edge-magic labeling . Furthermore, the edge-magic deficiency of a graph , , is defined as the smallest nonnegative integer such that has an edge-magic labeling. Similarly, the super edge-magic deficiency of a graph , , is either the smallest nonnegative integer such that has a super edge-magic labeling or if there exists no such integer . In this paper, we investigate the (super) edge-magic deficiency of chain graphs. Referring to these, we propose some open problems.

Suggested Citation

  • Ngurah Anak Agung Gede & Adiwijaya, 2017. "New Results on the (Super) Edge-Magic Deficiency of Chain Graphs," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-6, July.
    • Handle: RePEc:hin:jijmms:5156974
    DOI: 10.1155/2017/5156974
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