Des Welyyanti, Muhammad Rafif Fajri, Latifa Azhar Abel, Lyra Yulianti, Aisyah Nurinsani, Dony Permana
Chartrand et al. introduced the idea of the locating-chromatic number of connected graphs in 2002. Let c be a coloring of a graph H with k-colors. Let Si be the set of all vertices that get color i and let Π = {S1, S2, …, Sk } be the partition of V (H) induced by c. The color code cΠ (v) = (d(v, S1), d(v, S2), …, d(v, Sk)) of a vertex v ∈ H, where d(v, Si) = min{d(v, x) | x ∈ Si } and d(v, Si) < ∞ for all i ∈ [1, k]. 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 mCn. © 2026 The Authors.
Department of Mathematics and Data Sciences, Faculty of Mathematics and Natural Sciences, Universitas Andalas, West Sumatra, Padang, 25163, Indonesia; Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, West Java, Bandung, 40132, Indonesia; Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Padang, West Sumatra, Padang, 25171, Indonesia
