Global Domination in Bipolar Fuzzy Graphs

V. Mohanaselvi, S. Sivamani, N. Revathi

Abstract


In this paper the concept of global domination in bipolar fuzzy graph is introduced and studied its characterization. The necessary and sufficient condition for the global dominating set is given in terms of domination between the vertices. Also semi complete, purely semi complete, semi complementary and semi global domination concepts are defined and some results are obtained.

Keywords


Bipolar fuzzy graph (BFG); Strong edge; Dominating set; Domination number; Global dominating set; Global domination number; Semi complete; Purely semi complete; Semi complementary; Semi global dominating set and semi global domination number

Full Text:

PDF

References


M. Akram, Bipolar fuzzy graphs, Information Sciences 181 (2011), 5548 – 5564.

R.J. Hussain and S.Y. Mohamed, Global domination set in intuitionistic fuzzy graph, International Journal of Computational Engineering Research 4(9) (2014), 55 – 58

R.J. Hussain and S.Y. Mohamed, Semi global domination set in intuitionistic fuzzy graph, IOSR Journal of Mathematics 10(4) (Version II) (2014), 23 – 27

M.G. Karunambigai, M. Akram, K. Palanivel and S. Sivasankar, Domination in bipolar fuzzy graph, in Proceedings of the International Conference on Fuzzy Systems FUZZ-IEEE-2013, Hyderabad, India (2013), 1 – 6.

G.A. Nagoor, S.Y. Mohamed and J. Hussain, Semi global dominating set in fuzzy graphs, International Journal of Fuzzy Mathematical Archive 4(2) (2014), 115 – 122

G. Nirmal and M. Sheela, Global and factor domination in fuzzy graph, International Journal of Scientific and Research Publications 2(6) (2012), 1 – 4.

A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and their Applications to Cognitive and Decision Processes (Proc. U.S.-Japan Sem., Univ. Calif., Berkeley, Calif. (1974)), Academic Press, New York (1975), 77 – 95,

E. Sampathkumar, The global domination number of a graph, Jour. Math. Phy. Sc. 23 (5), 377 – 385.

L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338 – 353.




DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.946

eISSN 0975-5748; pISSN 0974-875X