On the Local Adjacency Metric Dimension of Generalized Petersen Graphs

Autor: Marsidi Marsidi, Dafik Dafik, Ika Hesti Agustin, Ridho Alfarisi
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Cauchy: Jurnal Matematika Murni dan Aplikasi, Vol 6, Iss 1, Pp 10-17 (2019)
Druh dokumentu: article
ISSN: 2086-0382
2477-3344
DOI: 10.18860/ca.v6i1.6487
Popis: 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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