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

  • Jaya Santoso Department of Informatics, Faculty of Informatics and Electrical Engineering, Institut Teknologi Del, Indonesia https://orcid.org/0009-0001-7329-3137
  • Darmaji Darmaji Department of Mathematics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss2pp791-804
Keywords: Cycle, Graph, Partition Dimension, Resolving Partition

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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Published
2025-04-01
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.
Issue
Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2025 Jaya Santoso, Darmaji Darmaji

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