TY - JOUR TI - On the Local Adjacency Metric Dimension of Generalized Petersen Graphs AU - Marsidi, Marsidi; Dafik, Dafik; Agustin, Ika Hesti; Alfarisi, Ridho IS - Vol 6, No 1 (2019): CAUCHY: Jurnal Matematika Murni dan Aplikasi PB - Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang JO - CAUCHY PY - 2019 SP - 10 EP - 17 UR - http://ejournal.uin-malang.ac.id/index.php/Math/article/downloadSuppFile/6487/579 AB - The local adjacency metric dimension is one of graph topic. Suppose there are three neighboring vertex , ,  in path . Path  is called local if  where each has representation: a is not equals  and  may equals to . Let’s say, .  For an order set of vertices , the adjacency representation of  with respect to  is the ordered -tuple , where  represents the adjacency distance . The distance  defined by 0 if , 1 if  adjacent with , and 2 if  does not adjacent with . The set  is a local adjacency resolving set of  if for every two distinct vertices ,  and  adjacent with y then . A minimum local adjacency resolving set in  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.