(1, 2)-Vertex Domination in Fuzzy Line Graphs

A (1, 2)-dominating set in a fuzzy graph G = (V, E) is a set S having the property that for every vertex v in V-S, there is at least one vertex in S at distance 1 from v and a second vertex in S at distance almost 2 from v. The minimum cardinality of (1, 2)-dominating set in fuzzy graph G is called the (1, 2)-domination number in G and we denote it by γ(1, 2). The fuzzy line graph L(G) of a fuzzy G =(V.E) is a graph with vertex set E(G) in which two vertices are adjacent if and only if the corresponding edges in G are adjacent. We introduce (1, 2)-domination number of a fuzzy line graph and obtain some interesting results for the new parameter in fuzzy graph.