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Face labelings of Klein-bottle fullerenes

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Abstract

The Klein-bottle fullerene is a finite trivalent graph embedded on the Klein-bottle such that each face is a hexagon. The paper deals with the problem of labeling the vertices, edges and faces of the Klein-bottle fullerene in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face and the weights of all 6-sided faces constitute an arithmetic progression of difference d. In this paper we study the existence of such labelings for several differences d.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions leading to improvement of this paper.

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Authors and Affiliations

  1. Department of Appl. Mathematics and Informatics, Technical University, Košice, Slovakia

    Martin Bača

  2. Abdus Salam School of Mathematical Sciences, GC University, 68-B, New Muslim Town, Lahore, Pakistan

    Martin Bača & Maria Naseem

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

    Ayesha Shabbir

Authors
  1. Martin Bača
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  2. Maria Naseem
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  3. Ayesha Shabbir
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Corresponding author

Correspondence to Martin Bača.

Additional information

The research for this article was supported by Slovak KEGA Grant 072TUKE-4/2014.

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Bača, M., Naseem, M. & Shabbir, A. Face labelings of Klein-bottle fullerenes. Acta Math. Appl. Sin. Engl. Ser. 33, 277–286 (2017). https://doi.org/10.1007/s10255-017-0658-1

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  • DOI: https://doi.org/10.1007/s10255-017-0658-1

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