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January 9, 2024
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November 15, 2024
Published
March 7, 2025
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Abstract

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.

Keywords

Locating-Coloring Locating-Chromatic Number Jellyfish Graphs

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How to Cite
Arfin, A. (2025). The Locating-Chromatic Number of Some Jellyfish Graphs. Journal of the Indonesian Mathematical Society, 31(1), 1627. https://doi.org/10.22342/jims.v31i1.1627
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