On (r; s)-Fuzzy Domination in Fuzzy Graphs

Let G = (sigma, mu) be a fuzzy graph on a finite set V : Let r; s epsilon [0; 1] and r < s: A fuzzy subset sigma(1) of sigma is called an (r; s)-fuzzy dominating set (r, s)-FD set) of G if (Sigma(mu(uv)>= r) sigma 1(u)) + sigma(1) (v) >= s for all v is an element of V. Then gamma(r; s) = min(sigma 1) [Sigma(x is an element of V) sigma(1) (x)] is called the (r, s)- fuzzy domination number of G; where the minimum is taken over all (r, s)-FD sets sigma(1) of G: In this paper we initiate a study of this parameter and other related concepts such as (r, s)-fuzzy irredundance and (r, s)-fuzzy independence. We obtain the dr; s_- fuzzy domination chain which is analogous to the domination chain in crisp graphs.