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Metric dimension of a graph is a well-studied concept. Recently, adjacency metric dimension of graph has been introduced. A set Q a ⊂ V G is considered to be an adjacency metric generator for G if u 1 , u 2 ∈ V \ Q a (supposing each pair); there must exist a vertex q ∈ Q a along with the condition that q is indeed adjacent to one of u 1 , u 2 . The minimum number of elements in adjacency metric generator is the adjacency metric dimension of G , denoted by di m a G. In this work, we compute exact values of the adjacency metric dimension of circulant graph C n 1 , 2 , Möbius ladder, hexagonal Möbius ladder, and the ladder graph. [ABSTRACT FROM AUTHOR]