Domination in fuzzy graphs – I

Product Intuitionistic Fuzzy Graph

“…2 (x, y) = 1 (x) 1 (y) and 2 (x, y) = 1 (x) 1 (y) for all x, y V. (1) and (3) we get 2 (x, y) = 2 (x, y) (4) If 1 normal, 1 (t) =1 for some t. Then (2) and (5) we get 2 (x, y) = 2 (x, y) (6) Now assuming that 2 k (x, y) = 2 (x, y) and 2 k (x, y) = 2 (x, y) we will prove 2 k+1 (x, y) = 2 (x, y) and 2 k+1 (x, y) = 2 (x, y) we have (u) 11 (v) (iv) from (iii) and (iv) we get (i) ( 12 + 22 )(u,v)= 12 (u,v) (v) and ( 11 + 21 )(u) ( 11 + 21 )(v)= 11 (u) 11 (v) (vi) from (v) and (vi) we get (ii) Therefore we get G 1 + G 2 is a product intuitionistic fuzzy sub graph of G. Similarly we can prove (u, v) X 1 . (u) 11 (v) and 12 (u, v) = 11 (u) 11 (v).…”

A Study on Double, Triple and N - Tuple Domination of Fuzzy Graphs

“…Several fuzzy analogs of graph theoretic concepts such as paths, cycle's connectedness etc., the concept of domination in fuzzy graphs was investigate and presents the concepts of independent domination, total domination, connected domination and domination in Cartesian product and composition of fuzzy graphs [19]. Several authors have studied the problem of obtaining an upper bound for the sum of a domination parameter and a graph theoretic parameter and characterized the corresponding extremal graphs.…”

A Study on Point Set Domination of Intuitionistic Fuzzy Graphs

“…Nagoor Gani, A and Sajitha Begum, S [3] defined degree, Order and Size in intuitionistic fuzzy graphs and extend the properties. The concept of Domination in fuzzy graphs is introduced by A. Somasundaram and S. Somasundaram [10] in the year 1998. Parvathi and Thamizhendhi [5] introduced the concepts of domination number in Intuitionistic fuzzy graphs.…”