On the Local Adjacency Metric Dimension of Generalized Petersen Graphs

Marsidi Marsidi, Dafik Dafik, Ika Hesti Agustin, Ridho Alfarisi

Abstract


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.


Keywords


Local Resolving Set; Local (Adjacency) Metric Dimension; Adjacency Metric Dimension; Generalized Petersen.

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References


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DOI: https://doi.org/10.18860/ca.v6i1.6487

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