New Domination Parameters in Fuzzy Graphs

C.Y.Ponnappan; R.Muthuraj; S. Basheer Ahamed

doi:https://doi.org/10.14445/22315373/IJMTT-V36P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 36 | Number 2 | Year 2016 | Article Id. IJMTT-V36P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P513

New Domination Parameters in Fuzzy Graphs

C.Y.Ponnappan, R.Muthuraj, S. Basheer Ahamed

Citation :

C.Y.Ponnappan, R.Muthuraj, S. Basheer Ahamed, "New Domination Parameters in Fuzzy Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 36, no. 2, pp. 99-102, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P513

Abstract

In this paper, regular domination, regular split domination in fuzzy graph, regular non split domination in fuzzy graph, regular connected domination in fuzzy graph and totally regular domination in fuzzy graph are introduced and discuss its properties. Also introduced inverse regular connected domination number. Furthermore this new domination parameter is compare with other known domination parameters.

Keywords

Regular domination, regular split domination number, regular non split domination number, regular connected domination, inverse regular connected domination.

References

[1] Harary, E., 1969. Graph Theory. Addison Wesley, Reading, MA. McAlester, M.L.N., 1988. Fuzzy intersection graphs. Comp. Math. Appl. 15(10), 871-886.
[2] Haynes, T.W., Hedetniemi S.T. and Slater P.J. (1998). Domination in Graphs: Advanced Topics, Marcel Dekker Inc. New York, U.S.A.
[3] Haynes, T.W., Hedetniemi S.T. and Slater P.J. (1998). Fundamentals of domination in graphs, Marcel Dekker Inc. New York, U.S.A.
[4] Kulli, V.R. and Janakiram B. (1997). The split domination number of graph. Graph Theory notes of New York. New York Academy of Sciences, XXXII, pp. 16-19.
[5] Mahioub.Q.M. and Soner.N.D (2007), “The split domination number of fuzzy graph “Accepted for publication in Far East Journal of Applied Mathematics”.
[6] Nagoor Gani.A and Radha.K, (2008). On Regular fuzzy Graphs. Journal of Physical sciences, Vol 12,2008,33-40.
[7] Hossein Rashmanlou and Madhumangal Pal., Some Properties of Highly Irregular Interval Valued Fuzzy Graphs, World Applied sciences journal 27 (12): 1756-1773,2013.
[8] Rosenfeld, A., 1975. Fuzzy graphs. In : Zadeh, L.A., Fu, K.S., Shimura, M. (Eds.), Fuzzy Sets and Their Applications. Academic Press, New York.
[9] Somasundaram, A., and Somasundaram, S., Domination in fuzzy graphs-I, Pattern Recognit. Lett. 19(9) 1998), 787-791.
[10] Ponnappan C.Y, Surulinathan .P, Basheer Ahamed .S, “The strong split domination number of fuzzy graphs” International Journal of Computer & Organization Trends – Volume 8 Number 1 – May 2014.
[11] Ponnappan C.Y, Surulinathan .P, Basheer Ahamed .S, “The strong split domination number of fuzzy graphs” International Journal of Computer & Organization Trends – Volume 8 Number 2 – May 2014.