Complete and Complementary Domination Number in Interval Valued Fuzzy Graphs

N.Sarala, T.Kavitha

Abstract: An interval-valued fuzzy graph of a graph G = (A, B) of a graph G = (V, E) is said to be complete if _ ( B) ^- (xy) =min {_ ( A) ^- (x), _ ( A) ^- (y) } and_ ( B) ^ ( +) (xy) =max{_ ( A) ^ ( +) (x), _ ( A) ^ ( +) (y) } for all xy E. Given a fuzzy graph, choose v V (G) and put S ={v}, For every v we have N (S) =V-S denoted by S is the complete dominating set. The minimum cardinality of a complete dominating set of interval valued fuzzy is called the complete domination number of G. we introduce complete and complementary domination number in interval valued fuzzy graphs and obtain some interesting results for this new parameter in interval valued fuzzy graphs.

Keywords: Dominating set, Domination in interval valued fuzzy graph, Fuzzy graphs, complete domination in interval valued fuzzy graphs, Complementary domination in interval valued fuzzy graphs