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A new algorithmic method to compute the chromatic number of Dihedral group

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Abstract

In this paper, we will compute the chromatic number of \(D_9\) , \(D_{15}\), and we will present an algorithm to compute the chromatic number of any Latin square of \(D_n\) (for all n) order.

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References

  1. Abel, R., Julian, R., Diana, Combe, Nelson, Adrian, M., Palmer, William D.: GBRDs with block size three over 2-groups, semi-dihedral groups and nilpotent groups. Electron. J. Comb. 18(1):Paper 32, 12, (2011)

  2. Besharati, N., Goddyn, L., Mahmoodian, E.S., Mortezaeefar, M.: On the chromatic number of Latin square graphs, volume 10486. Discret. Math. 339(11), 2613–2619 (2016)

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  3. Mortezaeefar, M.: Colorings of Latin square graphs and block designs. Master’s thesis, Sharif University of Technology, Tehran, Iran, (2009) (in Farsi, 23 Persian language)

  4. Shokri, K.: On the Latin square of groups and their coloring, Master’s thesis, Sharif University of Technology, Tehran, Iran, (2015) (in Farsi, 23 Persian language)

  5. Wanless, I.M.: Transversals in Latin squares: a survey. In: Surveys in Combinatorics 2011, London Math. Soc. Lecture Note Ser., vol. 392, pp. 403–437. Cambridge University Press, Cambridge (2011)

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Acknowledgements

I would like to thank the following individuals for their contribution: Dr. E. S. Mahmoodian for advising and mentorship in selecting the topic and supervising the progress; Mr. K. Shokri for the presentation of Dn group tables in his master degree thesis and checking the full colored table of \(D_9\) and \(D_{15}\) in our paper.

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Authors and Affiliations

  1. Department Mathematics, Islamic Azad University-South Tehran Branch, Tehran, Iran

    Azar Shokri & Maryam Golriz

Authors
  1. Azar Shokri
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  2. Maryam Golriz
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Correspondence to Maryam Golriz.

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Shokri, A., Golriz, M. A new algorithmic method to compute the chromatic number of Dihedral group. Math Sci 15, 145–151 (2021). https://doi.org/10.1007/s40096-020-00358-1

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  • DOI: https://doi.org/10.1007/s40096-020-00358-1

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