The Strong Split Domination Number of Fuzzy Graphs

  IJCOT-book-cover
 
International Journal of Computer & Organization Trends  (IJCOT)          
 
© 2014 by IJCOT Journal
Volume - 4 Issue - 3
Year of Publication : 2014
Authors :  C.Y.Ponnappan , P.Surulinathan , S. Basheer Ahamed
DOI :  10.14445/22492593/IJCOT-V8P301

Citation

C.Y.Ponnappan , P.Surulinathan , S. Basheer Ahamed. "The Strong Split Domination Number of Fuzzy Graphs", International Journal of Computer & organization Trends (IJCOT), V4(3):1-4 May - Jun 2014, ISSN:2249-2593, www.ijcotjournal.org. Published by Seventh Sense Research Group.

Abstract

A dominating set D of a fuzzy graph G=( ?,µ) is a strong split dominating set if the induced fuzzy subgraph H=(,??,µ?) is totally disconnected. The strong split domination number ?ss(G) of G is the minimum fuzzy cardinality of a strong split dominating set. In this paper we study a strong split dominating sets of fuzzy graphs and investigate the relationship of ?ss(G) or ?ss with other known parameter of G.

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. Kulli, V.R. and Janakiram B. (2000). The non-split domination number of graph. The Jounral of Pure and Applied Math. 31(5). Pp. 545-550.
6. Kulli, V.R. and Janakiram B. (2003). The strong non-split domination number of a graph. International Journal of Management and Systems. Vol. 19, No. 2, pp. 145-156.
7. Ore, O. (1962). Theory o Graphs. American Mathematical Society Colloq. Publi., Providence, RI, 38.
8. Q.M. Mahioub and N.D. Soner (2007), “The split domination number of fuzzy graph “Accepted for publication in Far East Journal of Applied Mathematics”.
9. Rosenfeld, A., 1975. Fuzzy graphs. In : Zadeh, L.A., Fu, K.S., Shimura, M. (Eds.), Fuzzy Sets and Their Applications. Aca-demic Press, New York.
10. Somasundaram, A., and Somasundaram, S., Domination in fuzzy graphs, Pattern Recognit. Lett. 19(9) 1998), 787-791.

Keywords
Fuzzy graphs, fuzzy domination, split fuzzy domination number, strong split fuzzy domination number.