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On Super Edge-Antimagicness of Circulant Graphs

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Abstract

A labeling of a graph is a mapping that carries some sets of graph elements into numbers (usually the positive integers). An \((a,d)\)-edge-antimagic total labeling of a graph \(G(V,E)\) is a one-to-one mapping \(f\) from \(V(G)\cup E(G)\) onto the set \(\{1,2,\dots , |V(G)|+|E(G)|\}\), such that the set of all the edge-weights, \(wt_f (uv) = f(u) +f(uv)+f(v)\), \(uv\in E(G)\), forms an arithmetic sequence starting from \(a\) and having a common difference \(d\). Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper we study the existence of such labelings for circulant graphs.

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Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions leading to improvement of this paper. The research for this article was supported by Slovak VEGA Grant 1/0130/12.

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Authors and Affiliations

  1. Department of Applied Mathematics and Informatics, Technical University, Kosice, Slovakia

    Martin Bača

  2. Faculty of Mathematics, COMSATS Institute of Information Technology, Wah Campus, Wah Cantt, Pakistan

    Yasir Bashir

  3. Faculty of Information Technology, University of Central Punjab, Lahore, Pakistan

    Muhammad Faisal Nadeem

  4. University College of Engineering, Sciences and Technology, Lahore Leads University, Lahore, Pakistan

    Ayesha Shabbir

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  1. Martin Bača
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  2. Yasir Bashir
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  3. Muhammad Faisal Nadeem
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  4. Ayesha Shabbir
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Correspondence to Martin Bača.

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Bača, M., Bashir, Y., Nadeem, M.F. et al. On Super Edge-Antimagicness of Circulant Graphs. Graphs and Combinatorics 31, 2019–2028 (2015). https://doi.org/10.1007/s00373-014-1505-2

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  • DOI: https://doi.org/10.1007/s00373-014-1505-2

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