CONNECTED DOMINATING SET IN 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
Keywords: Interval-valued fuzzy graph, connected dominating set, connected domi-nation number

Abstract

The connected domination is one of the important issues in mathematics and other science. In This paper, connected domination in interval-valued fuzzy graphs is defined and studied. Some bounds on connected domination number γc(G) is provided for sev- eral interval-valued fuzzy graphs. Furthermore, the relationship of γc(G) with some other known parameters in interval-valued fuzzy graphs are investigated with some suit- able examples.

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References

[1] M. Akram and W. A. Dudek, ”Interval-valued fuzzy graphs”, Cmput. Math. Appl. 61, (2011), 289-299.
[2] E. J. Cockayne and S. T. Hedetniemi, Towards a theory of domination in graphs, Net- works 7 (1977) 247-261.
[3] P. Debnath, Domination in interval-valued fuzzy graphs, Annals of Fuzzy Mathematics and Informatics. 6(2), (2013), 363-370.
[4] 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.
[5] O. T. Manjusha, M. S. Sunitha, connected domination in fuzzy graphs using strong arcs, Annals of Fuzzy Mathematics and Informatics, (2015), 1-16.
[6] H. Rashmanlou and Y. B. Jun, Complete interval valued Fuzzy graphs, Annals of Fuzzy Mathematics and Informatics, 3(1), (2013),107-130
[7] 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.
[8] E. Sampathkumar, H. B. Walikar, The connected domination number of a Graph, Jour.Math.Phy.Sci. 13(6), (1979).
[9] N. Sarala, P. Janaki, Connected domination number of fuzzy digraphs, research article IJSRR, 8(2), (2019), 4096-4100.
[10] Sarala N, Kavitha T. Strong (Weak) Domination in Interval Valued Fuzzy Graph. Dis- covery, 2016, 52(248), 1626-1634.
[11] A. Somasundaram, S. Somasundaran, ”Domination in fuzzy graphs-I”, Pattern Recog- nition Letters, 19, (1998), 787-791.
[12] A. Somasundaram, ”Domination in fuzzy graphs-II”, Journal of Fuzzy Mathematics, 20, (2000), 281-289.
[13] L. A. Zadeh, The concept of a linguistic and application to approximate reasoning I, Inform. Sci. 8, (1975), 149-249.
Published
2022-03-05
How to Cite
AL-Ahmadi, F. M., & Shubatah, M. M. Q. (2022). CONNECTED DOMINATING SET IN INTERVAL-VALUED FUZZY GRAPHS. IJRDO -JOURNAL OF MATHEMATICS, 8(2), 1-9. https://doi.org/10.53555/m.v8i2.4916