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Latifa Azhar Abel
Department of Mathematics and Data Sciences, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Padang, West Sumatra, 25163, Indonesia
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology Physics

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The Locating-Chromatic Number of Disjoint Union of Cycles Des Welyyanti; Muhammad Rafif Fajri; Latifa Azhar Abel; Lyra Yulianti; Aisyah Nurinsani; Dony Permana
Science and Technology Indonesia Vol. 11 No. 3 (2026): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2026.11.3.1046-1053

Abstract

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)=min{d(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.
Co-Authors Aisyah Nurinsani Des Welyyanti Dony Permana Muhammad Rafif Fajri Yulianti, Lyra