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Submitted
August 25, 2017
Accepted
May 31, 2018
Published
March 1, 2019
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Abstract

A cubic graph is a generalized structure of a fuzzy graph that gives moreprecision, flexibility and compatibility to a system when compared with systems thatare designed using fuzzy graphs. In this paper, some properties of an edge regularcubic graph are given. Particularly, strongly regular, edge regular and bi-regularcubic graphs are defined and the necessary and sucient condition for a cubic graphto be strongly regular is studied. Likewise, we have introduced a partially edgeregular cubic graph and fully edge regular cubic graph with suitable illustrations.Finally, we gave an application of cubic digraph in travel time.

Keywords

Cubic graph strongly regular cubic graph bi-regular cubic graph.

Article Details

Author Biography

Hossein Rashmanlou, Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Young Researchers and Elite Club, Central Tehran Branch,Islamic Azad University, Tehran, Iran
How to Cite
Krishna, K. K., Rashmanlou, H., Talebi, A. A., & Mofidnakhaei, F. (2019). Regularity Of Cubic Graph With Application. Journal of the Indonesian Mathematical Society, 25(1), 1–15. https://doi.org/10.22342/jims.25.1.607.1-15
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References

  1. M. Akram and W. A. Dudec, Interval-valued fuzzy graphs, Computers and
  2. Mathematics with Applications, 61 (2011), 289-299.
  3. P. Bhattacharya, Some remarks on fuzzy graphs, Pattern Recognition Letters, 6
  4. (1987), 297-302.
  5. J. Hongmei, W. Lianhua, Interval-valued fuzzy subsemigroups and subgroups
  6. sssociated by intervalvalued suzzy graphs, in: 2009 WRI Global Congress on
  7. Intelligent Systems, 2009,484-487.
  8. Y. B. Jun, Ch. S. Kim, K. O. Yang, Cubic sets, Annals of Fuzzy Mathematics and
  9. Informatics, 4 (1) (2012), 83-98.
  10. A. Kauman, Introduction a la theorie des sous-emsembles 503 flous, Masson et
  11. Cie 1 (1973).
  12. M. G. Karunambigai, K. Palanivel and S. Sivasankar, Edge regular intuitionistic
  13. fuzzy graph, Advances in Fuzzy Sets and Systems, 20 (1) (2015), 25-46.
  14. L. J. Kohout, W. Bandler, Fuzzy interval inference utilizing the checklist paradigm
  15. and BKrelational products, in: R.B. Kearfort et al. (Eds.), Applications of Interval
  16. Computations, Kluwer, Dordrecht, 1996, pp. 291-335.
  17. J. N. Mordeson, C. S. Peng, Operations on fuzzy graphs, Information Sciences, 79
  18. (1994), 159-170.
  19. J. N. Mordeson, P. S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs, Physica Verlag,
  20. Heidelberg, 1998. Second edition, 2001.
  21. H. Rashmanlou and M. Pal, Some properties of highly irregular interval-valued
  22. fuzzy graphs, World Applied Sciences Journal, 27 (12) (2013), 1756-1773.
  23. H. Rashmanlou, S. Samanta, M. Pal and R. A. Borzooei, A study on bipolar fuzzy
  24. graphs,Journal of Intelligent and Fuzzy Systems, 28 (2015), 571-580.
  25. H. Rashmanlou, S. Samanta, M. Pal and R. A. Borzooei, Bipolar fuzzy graphs with
  26. categorical properties, International Journal of Computational Intelligent Systems,
  27. (5) (2015), 808-818.
  28. A. Rosenfeld, Fuzzy graphs, in: L.A. Zadeh, K.S. Fu, M. Shimura (Eds.), Fuzzy
  29. Sets andTheir Applications, Academic Press, New York, 1975, pp. 77-95.
  30. R. Sambuc, Functions -Flous, Application alaide au Diagnostic en Pathologie
  31. Thyroidienne, These de Doctorat en Medecine, Marseille, 1975.
  32. M. S. Sunitha, A. Vijayakumar, Complement of a fuzzy graph, Indian Journal of
  33. Pure and Applied Mathematics, 33 (2002), 1451-1464.
  34. S. Samanta, M. Pal and M. Akram, m-step fuzzy competition graphs, Journal of
  35. Applied Mathematics and Computing, 47 (2015), 461472.
  36. S. Samanta and M. Pal, Fuzzy tolerance graphs, International Journal Latest Trend
  37. Mathematics, 1 (2) (2011), 57-67.
  38. S. Samanta and M. Pal, Fuzzy threshold graphs, CiiT International Journal of Fuzzy
  39. Systems, 3 (12) (2011), 360-364.
  40. S. Samanta and M. Pal, Fuzzy k-competition graphs and p-competition fuzzy graphs,
  41. Fuzzy Engineering and Information, 5 (2) (2013), 191-204.
  42. S. Samanta, M. Pal and A. Pal, New concepts of fuzzy planar graph, International
  43. Journal of Advanced Research in Artificial Intelligence, 3 (1) (2014), 52-59.
  44. I. B. Turksen, Interval-valued strict preference with Zadeh triples, Fuzzy Sets and
  45. Systems, 78 (1996), 183-195.
  46. L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
  47. L. A. Zadeh, The concept of a linguistic variable and its application to approximate
  48. reasoning-I, Information Sciences, 8 (1975), 199-249.