Let  be a graph with vertex set V and edge set E. The study of minimum number of points in a graph which will distinguish all the adjacent vertices in terms of distance between the vertices is given by the local metric basis problem. A subset W of V is said to be a local metric basis of G, if for any two adjacent vertices  there exists a vertex  such that  The minimum cardinality of local metric basis is called the local metric dimension of G and is denoted by  In this paper, we have determined the local metric dimension of some windmill graphs and sunlet graphs.

metric dimension, local metric dimension, windmill graph, Dutch windmill graph, sunlet graph.