<![CDATA[Abstract: For example G is a connected and nontrivial graph. The distance between two vertices u and v in G is the shortest path length between vertex u and v which is denoted by d (u, v). For an ordered set of of n vertex and v is a vertex in G, then the representation of vertex v to W is an ordered pair Set W is called as local distinguishing if for each pair of vertex u and v is adjacent to G. Local distinguishing set W with minimum cardinality is called as local metric base and the number of vertex on the local metric base of graph G is called as local metric dimension which is denoted by . In this study, the local metric dimension is determined on antiprism An graph and sun Sn graph. The results reveal that local metric dimension of antiprism graph is for . Local metric dimension of sun graph is for even n and for odd n.Keywords: local metric dimension, antiprism graph, sun graph, local distinguishing set.]]>
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