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Graph  G  is usually written by  G  = ( V, E ) is graph  G  where  V ( G ) is vertex set on graph  G  and  E ( G ) is edge set on graph  G . Graph  G  used in this study is only on simple and undirected graphs. Dominating set (DS) is graph  G  which have a vertex set  D , where each vertex in D can dominate the neighboring vertices, in other words every vertex from  u  ∈  V ( G ) −  D  is adjacent to verted  v  ∈  D . The minimum cardinality of dominating set is called by domination number, symbolized by  γ ( G ). Locating dominating set (LDS) is dominating set with additional condition. A graph  G  = ( V, E ) is said to be locating dominating set if the set of vertex dominator  D  satisfies every vertex that is not  D , that is  V  −  D  has a different intersection set with  D . The minimum cardinality of locating dominating set is called by locating domination number, symbolized by  γ L ( G ). In this paper we will determine the LDS on edge corona product. The edge corona product of graph is development of corona product graph. The edge corona of two graphs  G  and  H  is obtained by taking one copy of  G  and | E ( G )| copies of  H  and joining each end vertices of  i -th edge of  G  to every vertex in the  i -th copy of  H , symbolized by  G  ⋄  H . The results in this study are shown that there is a relation between the locating dominating set on the basic graph and its operation.

The locating dominating set (LDS) of generalized of corona product of path graph and any graphs