The Locating-Chromatic Number of Some Jellyfish Graphs - Arfin, Arfin (Journal of the Indonesian Mathematical Society, 2025)
Let c be a proper coloring of a graph G = (V, E) with k colors which induces a partition Π of V (G) into color classes L1, L2, . . . , Lk . For each vertex v in G, the color code cΠ(v) is defined as the ordered k-tuple (d(v, L1), d(v, L2), . . . , d(v, Lk )), where d(v, Li) represents the minimum distance from v to all other vertices u in Li(1 ≤ i ≤ k). If every vertex possesses unique color codes, then c is called a locating-k-coloring in G. If k is the minimum number such that c is a locating-k-coloring in G, then the locating-chromatic number of G is χL(G) = k. In this paper, the author determine the locating-chromatic number of some Jellyfish Graphs.