The Locating Chromatic Number of the Cyclic Chain Graph

The locating chromatic number of graph G (χL(G)) combines the idea of the partition dimension and the chromatic number by considering the locations of the vertices of graph G. Let (Cni, m) be a cyclic chain graph, namely a group of blocks in the form of a cycle graph Cn1(1), Cn2(2), ···, Cni(i). The ni is the number of vertices on the i-th cycle, and m is the number of cycles, for ni ≥ 3, 1 ≤ i ≤ m, and m ≥ 2, and the vertex vi,⌈ni/2⌉+1 in Cni(i) is identified with the vertex vi,⌈ni/2⌉+1 in Cni+1(i+1). In this research, we determine χL(Cni, m) for ni ≥ 3, 1 ≤ i ≤ m, and m ≥ 2.