Locating Chromatic Number for Rose Graphs and Barbell Operation

Authors

  • Riza Sawitri Department of Mathematics, Universitas Lampung
  • Lidwina Amelia Department of Mathematics, Universitas Lampung
  • Asmiati Asmiati Department of Mathematics, Universitas Lampung
  • Dina Eka Nurvazly Department of Mathematics, Universitas Lampung

DOI:

https://doi.org/10.29303/emj.v8i2.315

Keywords:

locating chromatic number, rose graph, barbell operation

Abstract

The locating chromatic number of a graph is the minimum color required for a locating coloring. This concept is a combination of partition dimension and vertex coloring of a graph. The purpose of this paper is to determine the locating chromatic number of the Rose graph and the barbell Rose graphs. The method used to obtain the locating chromatic number of a graph is by determining its upper and lower bounds. In this paper, the locating chromatic number of the Rose graphs and its barbell operation were obtained. The locating chromatic number of Rose graph 𝑀 (𝐶𝑛) is 4 for 𝑛 ∈ {3, 4} and 5 for 𝑛 ≥ 5. Furthermore, for barbell Rose graphs, 4 for 𝑛 = 3 and 5 for 𝑛 ≥ 4

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Published

2025-09-10

How to Cite

Sawitri, R., Amelia, L., Asmiati, A., & Nurvazly, D. E. (2025). Locating Chromatic Number for Rose Graphs and Barbell Operation. EIGEN MATHEMATICS JOURNAL, 8(2), 111–122. https://doi.org/10.29303/emj.v8i2.315

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