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Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Articles

ON THE LOCATING CHROMATIC NUMBER OF DISJOINT UNION OF BUCKMINSTERFULLERENE GRAPHS

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  • Debi Zulkarnain,
  • Lyra Yulianti,
  • Des Welyyanti,
  • Kiki Khaira Mardimar,
  • Muhammad Rafif Fajri
Debi Zulkarnain
Department of Mathematics and Science Data, Faculty of Mathematics and Natural Sciences Universitas Andalas, Indonesia
Lyra Yulianti
Department of Mathematics and Science Data, Faculty of Mathematics and Natural Sciences Universitas Andalas, Indonesia
Des Welyyanti
Department of Mathematics and Science Data, Faculty of Mathematics and Natural Sciences Universitas Andalas, Indonesia
Kiki Khaira Mardimar
Department of Mathematics and Science Data, Faculty of Mathematics and Natural Sciences Universitas Andalas, Indonesia
Muhammad Rafif Fajri
Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia
DOI: https://doi.org/10.30598/barekengvol18iss2pp0915-0922
Published May 25, 2024
Keywords
  • Locating-chromatic number,
  • Buckminsterfullerene graph,
  • Disjoint union of Buckminsterfullerene graphs
How to Cite
[1]
D. Zulkarnain, L. Yulianti, D. Welyyanti, K. Mardimar, and M. Fajri, “ON THE LOCATING CHROMATIC NUMBER OF DISJOINT UNION OF BUCKMINSTERFULLERENE GRAPHS”, BAREKENG: J. Math. & App., vol. 18, no. 2, pp. 0915-0922, May 2024.

Copyright (c) 2024 Debi Zulkarnain, Lyra Yulianti, Des Welyyanti, Kiki Khaira Mardimar, Muhammad Rafif Fajri

Creative Commons License

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

Abstract

Let  be a connected non-trivial graph. Let c be a proper vertex-coloring using k colors, namely . Let  be a partition of  induced by , where  is the color class that receives the color . The color code, denoted by , is defined as , where  for , and  is the distance between two vertices  and  in G. If all vertices in  have different color codes, then  is called as the locating-chromatic -coloring of . The locating-chromatic number of , denoted by , is the minimum  such that  has a locating coloring. Let   be the Buckminsterfullerene graph on   vertices. Buckminsterfullerene graph is a 3-connected planar graph and a member of the fullerene graphs, representing fullerene molecules in chemistry. In this paper, we determine the locating chromatic number of the disjoint union of Buckminsterfullerene graphs, denoted by .

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