The Locating-Chromatic Number of Disjoint Union of Cycles - Des Welyyanti; Muhammad Rafif Fajri; Latifa Azhar Abel; Lyra Yulianti; Aisyah Nurinsani; Dony Permana (Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya, 2026)
Chartrand et al. introduced the idea of the locating-chromatic number of connected graphs in 2002. Let c be a disconnected graph H with k-coloring. Let S_i be the set of all vertices that get color i and let Phi be the partition of V(H) induced by c. The color code C_Phi(v)=(d(v,S_1), d(v,S_2), ..., d(v,S_k)) of a vertex v, where d(v,S_k)=mind(v,x) . The locating k-coloring of H is denoted by c if all vertices in H have unique distinct color codes. Welyyanti et al. in 2014 expanded on this idea so that it also applies to unconnected graphs. In this work, for n=>3 and m=>2, we calculate the locating-chromatic number of the disjoint union of cycles, represented by mC_n.