On Strong(Weak) Domination in Fuzzy Graphs
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)γwf (G). 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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076738Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3622
 E.J. Cockayne and S.T. Hedetniemi,Towards a theory of domination in graphs, Networks,(1977), 247-261.
 Domke et. al,On parameters related to strong and weak domination in graphs,Discrete Mathematics 258 (2002), 1-11.
 T.W.Haynes et. al, Fundamentals of Domination in graphs, Marcel Dekker, New York, 1998.
 J.N. Mordeson and P.S. Nair, Fuzzy graphs and Fuzzy Hypergraphs, Physica Verlag, Heidelberg, 1998; second edition 2001.
 A. Rosenfeld Fuzzy graphs,in; L.A. Zadeh, K.S. Fu, M.Shimura(Eds.), Fuzzy sets and their Applications to Cognitive and Decision Processes, Academic Press, New York, 1975, 77-95.
 E. Sampathkumar, L. PushpalathaStrong, weak domination and domination balance in a graph, Discrete Math. 161(1996), 235-242.
 A. Somasundaram and S. Somasundaram,Domination in fuzzy graphs-I, Pattern recognition Letters 19(1998), 787-791.