International Journal of Engineering, Science and Mathematics Vol. 5 Issue 4, December 2016, ISSN: 2320-0294 Impact Factor: 6.765 Journal Homepage: http://www.ijmra.us , Email: editorijmie@gmail.com Double-Blind Peer Reviewed Refereed Open Access International Journal - Included in the International Serial Directories Indexed & Listed at: Ulrich's Periodicals Directory ©, U.S.A., Open J-Gage as well as in Cabell’s Directories of Publishing Opportunities, U.S.A 9 International Journal of Engineering, Science and Mathematics http://www.ijmra.us , Email: editorijmie@gmail.com (1, 2) -Vertex Domination in Fuzzy Line Graphs N.Sarala * T.Kavitha ** Abstract 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 (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. Keywords: Fuzzy graphs, (1,2)-dominating set in a fuzzy graph,(1,2)-domination number in a fuzzy graph, (1,2) - domination number in a fuzzy line graph. . * Associate Professor, Department of Mathematics, ADM College, Nagapattinam, Tamilnadu , India. ** Assistant professor, Department of Mathematics, EGSP Engineering College, Nagapattinam, Tamilnadu , India.