Vivi Ramdhani


Resolving partition is part of graph theory. Resolving partition is needed to obtain partition dimension. So far it has not been discussed regarding resolving partition of complete graphs. For this reason, this article explains the resolving partition of a complete graph.Given a connected graph  and  is a subset of   write . Suppose there is  then the distance between  to  is denoted in the form of . Then, suppose there is a partitioned set of , write , then we can obtain a  representation of  in the form of  The partition set  is called a resolving partition if the representation of each  ∈  with  is different. The minimum cardinality of the resolving -partition against  is called the partition dimension of , denoted by pd (). To get the partition dimension of a complete graph, first we find the resolving partition og the graph, resolving partition  orde  After that, to assist in obtaining the partition dimensions of complete graph, we explained that if is is a connected graph then  Based on these steps, finally obtained that the partition dimension of the complete graph, namely


Complete Graph, Partition Dimension, Resolving Partition


Chartrand, G, & Lesniak, L. (1979). Graph and Digraph. Kalifornia: A division of Wadsworf.Inc.

Chartrand, G, & Oellermann, O. R. (1993). Applied And Algorithmic Graph Theory. USA: United States Copyright Act.

Chartrand, Gary, Raines, M., & Zhang, P. (2000). The Directed Distance Dimension of Oriented Graphs. Mathematica Bohemica, 125(2), 155–168.

Chartrand, Gary, Salehi, E., & Zhang, P. (2000). The partition dimension of a graph. Aequationes Mathematicae, 59(1–2), 45–54. https://doi.org/10.1007/PL00000127

Chartrand, Gary, & Zhang, P. (2001). The Forcing Dimension of a Graph. Mathematica Bohemica, 126(4), 711–720.

Javaid, I., & Shokat, S. (2008). On the partition dimension of some wheel related graphs. Journal of Prime Research In, 4, 154–164.

Tomescu, I., & Imran, M. (2009). On Metric and Partition Dimensions of Some Infinite Regular Graphs. Bulletin Mathématique de La Société Des Sciences Mathématiques de Roumanie, 52(4), 461–472.

DOI: http://dx.doi.org/10.31958/js.v11i2.1610


  • There are currently no refbacks.

Copyright (c) 2019 Vivi Ramdhani

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

Indexed by:




Sainstek: Jurnal Sains dan Teknologi
ISSN 2085-8019  (print) | 2580-278x  (online)
Published by Institut Agama Islam Negeri Batusangkar

Email: sainstek@iainbatusangkar.ac.id

View Sainstek Stats


Creative Commons License

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