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Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Articles

THE LOCATING CHROMATIC NUMBER OF CHAIN(A,4,n) GRAPH

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  • Des Welyyanti,
  • Latifa Azhar Abel,
  • Lyra Yulianti
Des Welyyanti
Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia
Latifa Azhar Abel
Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia
Lyra Yulianti
Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss1pp353-360
Published January 13, 2025
Keywords
  • Chain Graph,
  • Color Code,
  • Locating Chromatic Number
How to Cite
[1]
D. Welyyanti, L. A. Abel, and L. Yulianti, “THE LOCATING CHROMATIC NUMBER OF CHAIN(A,4,n) GRAPH”, BAREKENG: J. Math. & App., vol. 19, no. 1, pp. 353-360, Jan. 2025.

Copyright (c) 2025 Des Welyyanti, Latifa Azhar Abel, Lyra Yulianti

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

Let  be a connected graph with a vertex coloringsuch that two adjacent vertices have different colors. We denote an ordered partition  where  is a color class with color-, consisting of vertices given color , for . The color code of a vertex  in  is a -vector: . where  is the distance between a vertex  in  and  for . If every two vertices  and  in  have different color codes, , then  is called the locating -coloring of . The minimum number of colors k needed in this coloring is defined as the locating chromatic number, denoted by . This paper determines the locating chromatic number of chain graph and the induction of two graphs . Graph  is a cyclic graph , which is the identification of , for n>2.

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