Partition Dimension of Dutch Windmill Graph

Dimensi Partisi Graf Kincir Angin Belanda untuk siklus orde besar

Authors

  • Hasmawati Hasmawati Hasanuddin University
  • Budi Nurwahyu
  • Ahmad Syukur Daming
  • Amir Kamal Amir

DOI:

https://doi.org/10.20956/j.v17i3.13596

Keywords:

Partition Dimension, Amalgamation, Cycle Graph

Abstract

Let be a connected graph G and -partition of  end . The coordinat to  is definition . If every twovertex is distinct  applies, then  is a called  partition of . The minimum k for which k-resolving partition of  is the partition dimension  and denoted with . In this paper, we investigates the partition dimensionfor a large Dutch windmill graph  for  and . We show that if  for some, forany.

References

Asmiati, 2012. Partition Dimension of Amalgamation of Stars. Bulletin of Mathematics. 02(04): 161-167.

Asmiati, 2016. Dimensi Partisi n Graf yang dihubungkan suatu lintasan. Jurnal Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Lampung. 19(3): 93-95.

Chartrand, G., dan Oellermann, O. R. 1993. Applied and Algorithmic graph Theory. McGraw–Hill, Inc, New York–St. Louis–San Francisco.

Chartrand, G., Salehi, E., dan Zang, P. 1998. On The Partition Dimension of Graph. Congressus Numerantium. Vol. 130: 157-168.

Chartrand, G., Salehi, E., dan Zang, P. 2000. The Partition Dimension of Graph. Aequationes Mathematicae. 59: 45-54.

Daming, A., S., Hasmawati, Haryanto, L., Nurwahyu B., 2020. Dimensi Partisi Graf Hasil Amalgamasi Siklus. Jurnal matematika, Statistika dan Komputasi, VOL.6, No.2, 199-207.

Darmaji, 2011. Dimensi Partisi Graf Multipartit dan Graf Hasil Korona Dua Graf Terhubung. Disertasi. Bandung: Institut Teknologi Bandung, Indonesia.

Diestel R. 2005. Graph Theory, Third Edition. Springer-Verlag Heidelberg. New York.

Fitriani, D., Salman, A. N. M. 2016. Rainbow connection number of amalgamation of some graphs. AKCE International Journal of Graphs and Combinatorics. 13 : 90–99.

Juan, R., Yero, I. G., dan Lemanska, M. 2014. On the Partition Dimension of Trees. Discrete Applied Mathematics. 166: 204-209.

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Published

2021-05-12

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Section

Research Articles

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