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Articles

Generalization of MacNeish’s Kronecker product theorem of mutually orthogonal Latin squares

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Pages 117-122 | Received 19 May 2020, Accepted 04 Aug 2021, Published online: 18 Aug 2021

References

  • Atef, M., El Atik, A. E. F, Nawar, A. (2021). Fuzzy topological structures via fuzzy graphs and their applications. Soft Comput. 25(8): 6013–6027.
  • Bose, R. C, Shrikhande, S. S. (1960). On the construction of sets of mutually orthogonal latin squares and the falsity of a conjecture of Euler. Trans. Amer. Math. Soc. 95(2): 191–209.
  • Bose, R. C., Shrikhande, S. S, Parker, E. T. (1960). Further results on the construction of mutually orthogonal latin squares and the falsity of Euler’s conjecture. Can. J. Math. 12: 189–203.
  • Colbourn, C. J, Dinitz, J. H. (2001). Mutually orthogonal Latin squares: A brief survey of constructions. J. Stat. Plan. Inference 95(1-2): 9–48.
  • El Atik, A. E. F., Nawar, A, Atef, M. (2020). Rough approximation models via graphs based on neighborhood systems. Granul. Comput.
  • El-Shanawany, R. (2001). Orthogonal double covers of complete bipartite graphs. Ph.D. dissertation, University of Rostock.
  • El-Shanawany, R. (2016). On mutually orthogonal graph-path squares. OJDM 06(01): 7–12.
  • El-Shanawany, R. (2016). On mutually orthogonal disjoint copies of graph squares. Note Mat. 36: 89–98.
  • El-Shanawany, R, El-Mesady, A. (2020). Mutually orthogonal graph squares for disjoint union of stars. ARS Combinatoria 149: 83–91.
  • El-Shanawany, R., El-Mesady, A, Shaaban, S. M. (2018). Mutually orthogonal graph squares for disjoint union of paths. AMS 12(7): 303–310.
  • Higazy, M. (2016). λ-Mutually orthogonal covers of complete bipartite graphs. AADM 17(2): 151–167.
  • Higazy, M., El-Mesady, A, Mohamed, M. S. (2020). On graph-orthogonal arrays by mutually orthogonal graph squares. Symmetry 12(11): 1895.
  • Keedwell, A. D, Dénes, J. (1974). Latin Squares and Their Applications. New York, NY; London, UK: Academic Press.
  • MacNeish, H. L. (1922). Euler squares. Ann. Math. 23(3): 221–227.
  • Sampathkumar, R, Srinivasan, S. (2009). Mutually orthogonal graph squares. J. Combin. Designs 17(5): 369–373.
  • Wilson, R. M. (1974). Concerning the number of mutually orthogonal latin squares. Discrete Math. 9(2): 181–198.