Fuzzy Graphs With Equal Fuzzy Domination And Independent Domination Numbers

A. Nagoorgani, P. Vijayalakshmi

Abstract


The basic definitions of fuzzy independent set, fuzzy dominating set,and fuzzy independent dominating sets are discussed. The aim of this paper is to find on what conditions the fuzzy graph has equal domination number and independent domination number. It is discussed briefly and also when the fuzzy graph is domination perfect is proved. Finally, the independent domination number for a connected fuzzy graph is obtained. 

Keywords


fuzzy dominating set; fuzzy independent dominating set; fuzzy domination and independent domination perfect; connected fuzzy graph.AMS Subject Classification 2010: 03E72; 05C69; 05C72

Full Text:

PDF PDF

References


Auer, D.B., Harary, F., Nieminen, J., and C.L. Suffel. Domination Alteration Sets in Graphs,Discrete Math., 47:153-161, 1983.

Bollobas, B., and Cockayne, E.J., Graph theoretic parameters concerning domination,independence and irredundance. J. Graph Theory, 3:241-250,1979.

Brigham, C., Chinn, Z., and Dutton, D., Vertex Domination – Critical Graphs, Networks, Vol. 18 (1988) 173-179.

Carrington, J.R., Harary, F., and Haynes, T.W., Changing and unchanging the domination number of a graph. J.Combin., Math. Combin. Comput., 9: 57-63, 1991.

Sumner, D.P., and Blitch, P., Domination critical graphs ,J.Combin, Theory Ser. B, 34:65-76, 1983.

Haynes, T., Hedetniemi,S.T., Slater, P.J., Fundamentals of domination in graph, Marcel Deckker, New York, 1998.

Fulman, T., A Note on the characterization of Domination Perfect graphs, J. Graph Theory, 17:47-51,1993.

Nagoorgani,A., and Chandrasekaran,V.T., Domination in fuzzy graph, Advances in fuzzy sets and system I(1)(2006), 17-26.

Nagoorgani, A., and Vadivel, P., Fuzzy independent dominating set, Adv. in Fuzzy sets and system 2(1) (2007), 99-108.

Nagoorgani,A., Vadivel,P., Relations between the parameters of Independent Domination and Irredundancein Fuzzy Graph, International Journal of


Refbacks

  • There are currently no refbacks.


International Conference on Engineering and Technology Development (ICETD)
Bandar Lampung University
ISSN: 2301-5690