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

  • Des Welyyanti Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia https://orcid.org/0000-0002-9614-8987
  • Latifa Azhar Abel Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia https://orcid.org/0009-0000-7352-1622
  • Lyra Yulianti Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia https://orcid.org/0000-0002-7982-121X
DOI: https://doi.org/10.30598/barekengvol19iss1pp353-360
Keywords: Chain Graph, Color Code, Locating Chromatic Number

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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Published
2025-01-13
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.
Issue
Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

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

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