Cauchy: Jurnal Matematika Murni dan Aplikasi (Dec 2019)
On the Local Adjacency Metric Dimension of Generalized Petersen Graphs
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.
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