THE LOCATING CHROMATIC NUMBER CRESCENT GRAPH {BS}_n FOR \ 1\le n\le10

Abstract

The locating chromatic number of a graph, denoted by $\chi_L (G)$, is the minimum number of colors required to color the vertices of a graph such that each vertex has a distinct color code. The crescent graph is a type of graph whose locating-chromatic number has not yet been determined. A crescent graph is formed from a circular graph shaped like a crescent moon, and two such crescent shaped graphs are joined together at a single common vertex. The crescent graph is denoted by $\(BS_n\)$. In this research, it was found that the locating chromatic number of the crescent graph $\chi_L(BS_n)$ for $1\le n\le 10$ is 4 for $n=1$ and 5 for $2\le n \le 10$. The method used includes defining the crescent graph, determining the locating coloring on the crescent graph, establishing the upper and lower bounds, and obtaining the exact value of the locating chromatic number of the crescent graph.