The local adjacency metric dimension is one of graph topic. Suppose there are three neighboring vertex , , Â in path . Path Â is called local if Â where each has representation: a is not equals Â and Â may equals to . Letâ€™s say, . Â For an order set of vertices , the adjacency representation of Â with respect to Â is the ordered -tuple , where Â represents the adjacency distance . The distance Â defined by 0 if , 1 if Â adjacent with , and 2 if Â does not adjacent with . The set Â is a local adjacency resolving set of Â if for every two distinct vertices , Â and Â adjacent with y then . A minimum local adjacency resolving set in Â is called local adjacency metric basis. The cardinality of vertices in the basis is a local adjacency metric dimension of , denoted by . Next, we investigate the local adjacency metric dimension of generalized petersen graph.
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