{"title":"On Strong(Weak) Domination in Fuzzy Graphs","authors":"C.Natarajan, S.K.Ayyaswamy","volume":43,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1035,"pagesEnd":1038,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/11138","abstract":"

Let G be a fuzzy graph. Then D Ôèå V is said to be a strong (weak) fuzzy dominating set of G if every vertex v ∈ V -D is strongly (weakly) dominated by some vertex u in D. We denote a strong (weak) fuzzy dominating set by sfd-set (wfd-set). The minimum scalar cardinality of a sfd-set (wfd-set) is called the strong (weak) fuzzy domination number of G and it is denoted by γsf (G)\u0002γwf (G)\u0003. In this paper we introduce the concept of strong (weak) domination in fuzzy graphs and obtain some interesting results for this new parameter in fuzzy graphs.<\/p>\r\n","references":" E.J. Cockayne and S.T. Hedetniemi,Towards a theory of domination in\r\ngraphs, Networks,(1977), 247-261.\r\n Domke et. al,On parameters related to strong and weak domination in\r\ngraphs,Discrete Mathematics 258 (2002), 1-11.\r\n T.W.Haynes et. al, Fundamentals of Domination in graphs, Marcel\r\nDekker, New York, 1998.\r\n J.N. Mordeson and P.S. Nair, Fuzzy graphs and Fuzzy Hypergraphs,\r\nPhysica Verlag, Heidelberg, 1998; second edition 2001.\r\n A. Rosenfeld Fuzzy graphs,in; L.A. Zadeh, K.S. Fu, M.Shimura(Eds.),\r\nFuzzy sets and their Applications to Cognitive and Decision Processes,\r\nAcademic Press, New York, 1975, 77-95.\r\n E. Sampathkumar, L. PushpalathaStrong, weak domination and domination\r\nbalance in a graph, Discrete Math. 161(1996), 235-242.\r\n A. Somasundaram and S. Somasundaram,Domination in fuzzy graphs-I,\r\nPattern recognition Letters 19(1998), 787-791.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 43, 2010"}