Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Articles

THE PARTITION DIMENSION OF CYCLE BOOKS GRAPH B_(m,n) WITH A COMMON PATH P_2

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  • Jaya Santoso,
  • Darmaji Darmaji
Jaya Santoso
Department of Informatics, Faculty of Informatics and Electrical Engineering, Institut Teknologi Del, Indonesia
Darmaji Darmaji
Department of Mathematics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss2pp791-804
Published April 1, 2025
Keywords
  • Cycle,
  • Graph,
  • Partition Dimension,
  • Resolving Partition
How to Cite
[1]
J. Santoso and D. Darmaji, “THE PARTITION DIMENSION OF CYCLE BOOKS GRAPH B_(m,n) WITH A COMMON PATH P_2”, BAREKENG: J. Math. & App., vol. 19, no. 2, pp. 791-804, Apr. 2025.

Copyright (c) 2025 Jaya Santoso, Darmaji Darmaji

Creative Commons License

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

Abstract

Suppose  is a connected graph with  elements of a set of vertices  denoted by  and  a subset of . The distance between  and  is the shortest distance  to every vertex  in . Let  be a partition of , where each subset  belongs to . The representation of a vertex  with respect to  is defined as the set of distances from  to each vertex in . If each representation of each vertex of  is different, then the partition  is called the resolving partition of , and the partition dimension  is the smallest integer  such that  has a resolving partition with  members. In this research, we show the partition dimensions of the cycle books graph . Cycle books graph  is a graph consisting of  copies of a cycle with a common path . The partition dimension of the cycle books graph  for  and  is shown.

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