Double domination on bipolar fuzzy graphs with strong edge and its properties

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DOI:

https://doi.org/10.26637/MJM0804/0043

Abstract

In this article, the definition of double dominance is introduced in the bipolar fuzzy graph. It provides descriptions of the size, order, degree etc of a bipolar fuzzy graph. With sufficient examples, the double dominance number of a bipolar fuzzy graph has been clarified. It addresses the properties of double dominance on the bipolar fuzzy graph. Some simple theorems have also been proposed relating to the claimed supremacy.

Keywords:

Bipolar fuzzy graph, dominating set, double dominating set, doubledomination number on bipolar fuzzy graph

Mathematics Subject Classification:

Mathematics
  • R. Muthuraj PG and Research Department of Mathematics, H.H. The Rajah’s College, Pudukkottai–622 001, Tamil Nadu, India.
  • A. Kanimozhi Research Scholar, PG and Research Department of Mathematics, H.H. The Rajah’s College, Pudukkottai–622 001, Tamil Nadu, India.
  • Pages: 1583-1586
  • Date Published: 01-10-2020
  • Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

Basheer Ahamed Mohideen, Types of Degrees in Bipolar Fuzzy Graphs, Applied Mathematical Sciences, 7(98)(2013), 4857-4866.

F. Haray, T. W. Haynes, Double domination in Graphs, Arscornsin, 55(2000), 201-213.

Hossein Rashmanalou, SovanSamanta, Madhumangal pal and RajabaliBozzarei, A study on bipolar fuzzy graphs, Journal of Intelligent and Fuzzy systems, 28(2015), 571-580.

M. G Karunambigai, Muhammed Akram, PalanivelKasilingam, Sivakumar Shanmugam, Domination in Bipolar Fuzzy Graphs, Fuzz-IEEE International Conference on Fuzzy System, July 7-10-2013, Hyderabad, India.

Muhammad Akram, Bipolar Fuzzy graphs, Information Sciences, 181(2011), 5548-5564.

Muhammad Akram, A. Wieslaw Dudek, Regular bipolar fuzzy graphs, Neural comput & Appl., 21(1)(2012), S197S205.

R. Muthuraj, A. Kanimozhi, Equitable total domination on bipolar fuzzy graph, Journal of Critical Reviews, $7(15)(2020), 4038-4046$.

A. NagoorGani, V. T. Chandrasekaran, Domination in Fuzzy Graph, Adv. In Fuzzy Sets and Systems, 1(1)(2006), $17-26$.

A. NagoorGani, Muhammed Akram and S. Anupriya, Double domination on Intuitionistic fuzzy Graphs, J. Appl. Math. Comput., DOI 10.1007/s12190-015-09520.

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.

A. Somasundaram, S. Somasundaram, Domination in Fuzzy Graphs-I, Pattern Recognition Letters, 19(1998), $787-791$.

Teresa W. Haynes, Stephen T. Hedetniemi, Peter J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998.

L. A. Zadeh, Fuzzy Sets, Information Sciences, 8(1965), $338-353$.

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Published

01-10-2020

How to Cite

R. Muthuraj, and A. Kanimozhi. “Double Domination on Bipolar Fuzzy Graphs With Strong Edge and Its Properties”. Malaya Journal of Matematik, vol. 8, no. 04, Oct. 2020, pp. 1583-6, doi:10.26637/MJM0804/0043.