Inverse Edge Domination in Fuzzy Graphs

C.Y.Ponnappan; S.Basheer Ahamed; P.Surulinathan

doi:https://doi.org/10.14445/22315373/IJMTT-V20P513

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 20 | Number 2 | Year 2015 | Article Id. IJMTT-V20P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V20P513

Inverse Edge Domination in Fuzzy Graphs

C.Y.Ponnappan, S.Basheer Ahamed, P.Surulinathan

Citation :

C.Y.Ponnappan, S.Basheer Ahamed, P.Surulinathan, "Inverse Edge Domination in Fuzzy Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 20, no. 2, pp. 103-109, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V20P513

Abstract

In this paper we discuss the concepts of inverse edge domination and total edge domination in fuzzy graph. We determine the inverse edge domination number ýI(G) and the total edge domination number ýt (G) for several classes of fuzzy graph and obtain bounds for the same. We also obtain Nordhaus – Gaddum type resuts for these parameters.

Keywords

Fuzzy graph, Edge domination, Inverse edge domination, Total edge Domination, Total inverse edge 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. Ore, O. (1962). Theory of Graphs. American Mathematical Society Colloq. Publi., Providence, RI, 38.
6. Ponnappan.C.Y.,.Basheer Ahamed.S and Surulinathan.P.,Edge domination in fuzzy graph – new approach, International journal of IT,Engg&Applied sciences Research.Vol 4,No.1,Jan (2015)
7. Ponnappan.C.Y.,.Basheer Ahamed.S and Surulinathan.P.The Split,Edge domination in fuzzy graphs,Int.Jour.of Mathematics Trends and Tech.Vol 18,No 1 Feb(2015)
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., D