The Partition Dimension on the Grid Graph

Authors

  • Haspika Haspika Universitas hasanuddin
  • Hasmawati Hasmawati
  • Naimah Aris

DOI:

https://doi.org/10.20956/j.v19i2.23904

Keywords:

grid graph, partition dimensions, resolving partition, partition set

Abstract

Graph G is a discrete set pair with the notation V(G)   with its element called a vertex and the set of different and unordered pairs with the notation E(G)   where the element is called edge. One type of graph Gm,n is a grid graph that is notated  is a graph of the result of the operation between two path graphs (Pm*Pn).  The set of partition∏ ={S1,S2,…,Sk} of V(G) is called a resolving partition if its representation for each vertex on graph G is different. The cardinality of the minimum resolving partition of graph G is the partition dimension of the graph G denoted pd(G). This paper discusses the dimension of the grid graph partition Gm,n  with the result pd(Gm,n) = 3 for m,n>=2 with n even value.

 

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Published

2023-01-05

Issue

Vol. 19 No. 2 (2023): JANUARY 2023

Section

Research Articles

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Copyright (c) 2023 Author and publisher

Creative Commons License

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

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

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