Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Vertex Antimagic Total Labeling of Digraphs

  • PANDIMADEVI, J. (Department of Mathematics, EMG Yadava women's College) ;
  • SUBBIAH, S.P. (Department of Mathematics, Mannar Thirumalai Naicker College)
  • Received : 2014.03.03
  • Accepted : 2014.10.17
  • Published : 2015.06.23
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Abstract

In this paper we investigate the properties of (a, d)-vertex antimagic total labeling of a digraph D = (V, A). In this labeling, we assign to the vertices and arcs the consecutive integers from 1 to |V|+|A| and calculate the sum of labels at each vertex, i.e., the vertex label added to the labels on its out arcs. These sums form an arithmetical progression with initial term a and common difference d. We show the existence and non-existence of (a, d)-vertex antimagic total labeling for several class of digraphs, and show how to construct labelings for generalized de Bruijn digraphs. We conclude this paper with an open problem suitable for further research.

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References

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