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.

Keywords

• local resolving set
• local (adjacency) metric dimension
• adjacency metric dimension
• generalized petersen.