Let G = (V, μ, σ) be a fuzzy graph on a finite set V. A fuzzy subset μ′ of μ is called a fuzzy dominating set of G if,
Fuzzy domination number γfz is defined accordingly. In this paper we initiate a study of this parameter. Some properties of fuzzy dominating sets are studied and fuzzy domination number γfz is determined for some graphs.
RosenfeldA., Fuzzy graphs. Fuzzy Sets and their Applications to Cognitive and Decision Processes, 77–95. Academic Press.1975.
2.
SomasundaramA. and SomasundaramS., Domination in fuzzy graphs –. i. Pattern Recognition Letters19(9) (1998), 787–791.
3.
GaniN. and ChandrasekaranV.T., Domination in fuzzy graph, Advances in Fuzzy Sets and Systems 1, 012006.
4.
ManjushaO.T. and SunithaM.S., Strong domination in fuzzy graphs, Fuzzy Information and Engineering7(3) (2015), 369–377.
5.
MordesonJ.N., and Premchand S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs, Physica- Verlag2000
6.
BhutaniK. and RosenfeldA., Strong arcs in fuzzygraphs, Inf Sci152 (2003), 319–322.
7.
ManjushaO.T. and SunithaM., Notes on domination in fuzzy graphs, Journal of Intelligent and Fuzzy Systems27 (2014), 3205–3212.
8.
WimerT.V., HedetnemiS.M. and HedetniemiS.T., Linear time resourse allocation algorithms for trees. Technical Report URL-014, Department of Mathematics, Clemson University1987.
9.
HedetniemiS.T., MynhardtC.M., CockayneE.J. and FrickeG., Properties of minimal dominating functions of graphs, Technical Report, DMS-547-IR1990.
10.
BhutaniK., ArumugamS. and SathikalaL., On (r,s)-fuzzy domination in fuzzy graphs, New Mathematics and Natural Computation12(01) (2016), 1–10.
