Some Topics on Critical Arc and Insensitive Node Domination in a Fuzzy Graph

A subset D of V is said to be a fuzzy dominating set of G if for every v V – D, there exists u D such that u dominates v. The minimum cardinality taken over all dominating sets in G is the domination number γ(G). Here the critical arc domination is discussed in the following sense: For each node u, v є D with u and v are not adjacent then γ(G + e) < γ(G) for e = uv an arc between u and v. The existence of such fuzzy graph and it properties are discussed. Finally, insensitive node of fuzzy graph is discussed (i.e) if any node is removed from G then its domination does not change.