TOTAL PERFECT DOMINATION OF AN INTERVAL-VALUED FUZZY GRAPHS

  • Faisal M. AL-Ahmadi Departement of Mathematics, Sheba Region University, Faculty of Education, Arts and Science Marib, Yemen
  • Mahiuob M. Q. Shubatah Department of Mathematics, Faculty of Science and Education, Albaydha University, Albaydha, Yemen
  • Yahya Q. Hasan
DOI: https://doi.org/10.53555/m.v8i2.4917
Keywords: Interval-valued fuzzy graph, total dominating set, perfect dominating set, total Perfect dominating set, total perfect domination number

Abstract

 A perfect dominating set Dp of an interval-valued fuzzy graph G = (A, B) of G∗ = (V, E) is called a total perfect dominating set of G if every vertex of G is domi- nates to at least one vertex of Dp and denoted by Dtp. In This article, the new kind of parameter total perfect domination in interval-valued fuzzy graphs is defined and stud- ied. We research and concludes Some bounds on total perfect domination number γtp(G) and Γtp(G) for several classes in interval-valued fuzzy graphs and obtained. Finally we introduce characteristics between the total perfect domination and perfect domination, total domination and connected in interval-valued fuzzy graphs.

Downloads

Download data is not yet available.

References

[1] M. Akram and W. A. Dudek, ”Interval-valued fuzzy graphs”, Cmput. Math. Appl. 61, (2011), 289-299.
[2] F. M. Al-Ahmadi, M. M. Q. Shubatah. Perfect dominating set of an interval-valued fuzzy graphs, Asian journal of Probability and Statistics, 11(4), (2021), 35-46.
[3] E.J. Cockayne, R.M. Dawes, and S.T. Hedetniemi, Total dominations in graphs, Net- works, 10 (1980), 211-219.
[4] E. J. Cockayne and S. T. Hedetniemi, Towards a theory of domination in graphs, Net- works 7 (1977) 247-261.
[5] P. Debnath, Domination in interval-valued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics. 6(2), (2013), 363-370.
[6] H. Ju and L. Wang, Interval-valued fuzzy sub semi groups and subgroups associated by interval-valued fuzzy graphs, in Proceedings of the WRI Global Congress on Intelligent Systems (GCIS 09), pp. 484487, Xiamen, China, May 2009.
[7] M. Naga Maruthi Kumari and R. Chandrasekhar, ”Operations on interval-valued fuzzy graphs”, IJARSE; 4(4), (2015), 618-627.
[8] O. T. Manjusha and M. S. Sunitha, connected domination in fuzzy graphs using strong arcs, Annals of Fuzzy Mathematics and Informatics, (2015), 1-16.
[9] O. T. Manjusha and M. S. Sunitha, Total Domination in Fuzzy Graphs using strong arcs, Annals of Pur and Applied Mathematics. 9(1), (2015), 23-33.
[10] A. M. Philip. Interval-valued fuzzy bridges and interval-valued fuzzy cutnodes. Annals of Pure and Applied Mathematics, 14(3), (2017), 473-487.
[11] A. M. Philip, S. J. Kalayathankal and J. V. Kureethara. On different kinds of arcs in interval valued fuzzy graphs. Malaya Journal of Mathematik,7(2), (2018), 309-313.

[12] A. M. Philip, S. J. Kalayathankal and J. V. Kureethara: On some matrices associated with interval-valued fuzzy graph, NTMSCI 7, No. 3, (2019), 268-277.
[13] C.Y.Ponnappan, S.Basheer Ahamed and P.Surulinathan, Connected Edge domination in fuzzy graph new approach, International journal of IT, Engg and Applied science Research, 4(1)(2015), 133-137.
[14] H. Rashmanlou and Y. B. Jun, Complete interval valued Fuzzy graphs, Annals of Fuzzy Mathematics and Informatics, 3(1), (2013), 107-130.
[15] S.Revathi, P.J.Jayalakshmi, C.V.R.Harinarayanan Perfect Dominating Sets in fuzzy graphs IOSR Journal of Mathematics, 8(3), (2013), 43-47.
[16] S.Revathi, R. Muthuraj and C.V.R.Harinarayanan Connected Perfect Dominating Sets in fuzzy graph Golden Research thoughts, Vol-5. (2015), 1-5.
[17] A. Rosenfeld, Fuzzy graphs, In. L. A. Zadeh, K. S. Fu and M. Shimura, (Eds). ”Fuzzy Sets and their Applications”, Academic Press, New York, (1975), 77-95.
[18] E. Sampathkumar, H. B. Walikar, The connected domination number of a Graph, Jour.Math.Phy.Sci. 13(6), (1979).
[19] N. Sarala, P. Janaki, Connected domination number of fuzzy digraphs, research article IJSRR, 8(2), (2019), 4096-4100.
[20] N. Sarala, T. Kavitha, Complete and Complementary Domination Number in Interval Valued Fuzzy Graphs. IJSR, 5 (2016), 2046-2050.
[21] N. Sarala, T. Kavitha, Strong (Weak) Domination in Interval Valued Fuzzy Graph. Dis- covery, 52(248), (2016), 1626-1634.
[22] A. Somasundaram, S. Somasundaran, ”Domination in fuzzy graphs-I”, Pattern Recog- nition Letters, 19, (1998), 787-791.
[23] A. Somasundaram, ”Domination in fuzzy graphs-II”, Journal of Fuzzy Mathematics, 20, (2000), 281-289.
[24] L. A. Zadeh, The concept of a linguistic and application to approximate reasoning I, Inform. Sci. 8, (1975), 149-249.
Published
2022-03-10
How to Cite
AL-Ahmadi, F. M., Shubatah, M. M. Q., & Hasan, Y. Q. (2022). TOTAL PERFECT DOMINATION OF AN INTERVAL-VALUED FUZZY GRAPHS. IJRDO -JOURNAL OF MATHEMATICS, 8(2), 10-41. https://doi.org/10.53555/m.v8i2.4917
Issue
Vol. 8 No. 2 (2022): JOURNAL OF MATHEMATICS (ISSN: 2455-9210)
Section
Articles

Copyright (c) 2022 IJRDO - Journal of Mathematics (ISSN: 2455-9210)

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Author(s) and co-author(s) jointly and severally represent and warrant that the Article is original with the author(s) and does not infringe any copyright or violate any other right of any third parties, and that the Article has not been published elsewhere. Author(s) agree to the terms that the IJRDO Journal will have the full right to remove the published article on any misconduct found in the published article.