Abstract
Metric dimension of a graph is a well-studied concept. Recently, adjacency metric dimension of graph has been introduced. A set Q(a )subset of V(G) is considered to be an adjacency metric generator for G if u(1),u(2)is an element of V\Q(a) (supposing each pair); there must exist a vertex q is an element of Q(a) along with the condition that q is indeed adjacent to one of u1,u(2). The minimum number of elements in adjacency metric generator is the adjacency metric dimension of G, denoted by dim(a)(G). In this work, we compute exact values of the adjacency metric dimension of circulant graph C-n(1,2), Mobius ladder, hexagonal Mobius ladder, and the ladder graph.