Let be a simple, finite, and connected graph.An ordered set of vertices of a Creamers nontrivial connected graph is and the -vector represent vertex that respect to , where and is the distance between vertex and for.The set called a resolving set for if different vertex of have different representations that respect to.The minimum of cardinality of resolving set of G is the metric dimension of , denoted by.
In this paper, we give the local metric dimension of some operation graphs such as joint graph , amalgamation Juice of parachute, amalgamation of fan, and.