On the Local Adjacency Metric Dimension of Generalized Petersen Graphs

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


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.


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

Full Text:



J. L. Gross, J. Yellen and P. Zhang, Handbook of graph Theory, Second Edition CRC Press Taylor and Francis Group, 2014.

G. Chartrand and L. Lesniak, Graphs and digraphs 3rd ed London: Chapman and Hall, 2000.

J. A. Rodriguez-Velazquez and H. Fernau, "On the (adjacency) metric dimension of corona and strong product graphs and their local variants", Combinatorial and Computational Results, Arxiv: 1309.2275.v1[math.CO].

A. Y. Badri and Darmaji, ”Local adjacency metric dimension of sun graph and stacked book graph”, Journal of Physics: Conf. Series, vol. 974, No. 012069, pp. 01-05, 2018.

Rinurwati, H. Suprajitno, and Slamin, ”On local adjacency metric dimension of some wheel related graphs with pendant points”, AIP Conference Proceedings, vol. 1867, No. 020065, pp. 01-06, 2017.

Marsidi, M., Dafik, D., Agustin, I. H., & Alfarisi, R. (2016). On the local metric dimension of line graph of special graph. Cauchy, 4(3), 125-130.

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


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Jalan Gajayana 50 Malang, Jawa Timur, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.