Locating Chromatic Number for Rose Graphs and Barbell Operation - Riza Sawitri; Lidwina Amelia; Asmiati Asmiati; Dina Eka Nurvazly (University of Mataram, 2025)
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 ð‘€ (ð¶ð‘›) is 4 for ð‘› âˆˆ 3, 4 and 5 for ð‘› â‰¥ 5. Furthermore, for barbell Rose graphs, 4 for ð‘› = 3 and 5 for ð‘› â‰¥ 4