Local Antimagic Edge Coloring Of Gear Graphs And Semi Parachute Graphs


DOI:
https://doi.org/10.32665/james.v8i2.4775Keywords:
Chromatic, Edge Coloring, Gear, Local Antimagic, Semi ParachuteAbstract
The graph G is a pair of sets consisting of a vertex set V(G) and an edge set E(G), denoted by G = (V (G),E(G)). Coloring a graph involves assigning colors to each vertex, edge, or region such that no adjacent vertices, edges, or regions share the same color. A bijective function f∶ V (G) → {1,2,3,...,|V (G)|} is called a local edge antimagic coloring if for any two adjacent edges e_1 and e_2, they have different weights, w(e_1) ≠ w(e_2), where e = uv ∈ E(G) and w(e) = f (u)+f (v). The chromatic number is the term used in the context of local antimagic coloring, referring to the minimum number of colors derived from local antimagic labeling. This research discusses the local antimagic edge coloring on the Gear Graph (G_n) and the Semi Parachute Graph (SP_(2n-1)). The aim of the research is to determine the chromatic number of local antimagic edge coloring χlea(G) for the researched graphs. The method used in this research is pattern detection to derive the general pattern. Based on the analysis, the chromatic number of local antimagic edge coloring is obtained for the Gear Graph (G_n) and the Semi Parachute Graph (SP_(2n-1)) are χlea (G_n)=n + 2 and χlea(SP_(2n-1) )=n+ 2.
References
Agustin, I.H., Hasan, M., Dafik., Alfarisi, R., Kristiana, A.I., Prihandini, R.M. (2018). Local Edge Antimagic Coloring of Comb Product of Graphs. Journal of Physics: Conference Series. Vol. 1008. doi :10.1088/1742-6596/1008/1/012038
Agustin, I.H., Kurniawati, E.Y., Dafik., Alfarisi. R. (2018). Super Local Edge Antimagic Total Coloring of P_n⊳H. Journal of Physics: Conference Series. Vol. 1008. DOI:10.1088/1742-6596/1008/1/012036
Agustin, I.H., Moh, Hasan., Dafik., Ridho, A., dan Prihandini, R.M. (2017). Local Edge Antimagic Coloring of Graphs. Far East Journal Of Mathematical Science (FJMS). Vol. 102. No. 9. http://dx.doi.org/10.17654/MS102091925
Agustin, I.H., Moh, Hasan., Dafik., Ridho, A., dan Prihandini, R.M. (2017). Local Edge Antimagic Coloring of Comb Product of Graphs. Far East Journal Of Mathematical Science (FJMS). DOI:10.1088/17426596/1008/1/012038.
Arumugam, S., Premalatha, K., Baca, M., dan Andrea, S.F. (2017). Local Antimagic Vertex Coloring of a Graph. Graph and Combinatorics, 33, 275- 285. http://dx.doi.org/10.1007/s00373-017-1758-7.
Daniel, F., dan Taneo, P.NL. (2019). Teori Graf. Sleman : Deepublish.
Gallian, J.A. (2022). A Dynamic Survey of Graph Labelling. The Journal of Combinatorics. Vol. 25
Kaindi, Y.P., Desi, F.P., Wasono. (2023). Pewarnaan Lokal Wilayah Super Antimagic Total Pada Graf Tangga dan Graf Tiga Tangga Melingkar. Journal of Mathematics Education and Science. Vol.6. No.2. https://doi.org/10.32665/james.v6i2.1929 .
Masitah, Lioni. (2013). Definisi Sisi-Ajaib Super Dari Graf Kipas. Jurnal Matematika UNAND. Vol. 3. No. 2. https://doi.org/10.25077/jmu.2.3.121-125.2013
Munir, R. (2010). Matematika Diskrit. Bandung: Informatika.
Nisviasari, R., Dafik, Agustin, I.H., Prihandini, R.M., Maylisa, I.N. (2019). Local Super Antimagic Total Face Coloring of Planar Graphs. IOP Conf. Series : Earth and Environmental Science.
Nisviasari, R., Dafik, Agustin, I.H., Prihandini, R.M., Maylisa, I.N. (2021). Local Super Antimagic Total Face Coloring of Shackle Graphs. Journal of Physics : Conference Series.
Parkhurst, H. (2014). Pelabelan Total (a, d)− Sisi Anti Ajaib Super padaGabungan Graf Lengkap mKn. Jurnal Matematika UNAND. Vol. 3. No. 4. https://doi.org/10.25077/jmu.3.4.24-27.2014
Putri, D.F., Dafik, Agustin. I.H., Ridho, A. (2018). On The Local Vertex Antimagic Total Coloring Of Some Families Tree. Journal of Physics: Conference Series. https://doi.org/10.1088/1742-6596/1008/1/012035.
Waluyo, E., Abdul, A.W., Moh, Rudi. (2023). Pewarnaan Graceful pada Graf Hasil Comb Siklus dan Graf Star. KadikmA. Vol. 14. No. 1. DOI:10.19184/kdma.v14i1.38552
Downloads
Published
How to Cite
Issue
Section
Categories
License
Copyright (c) 2025 Journal of Mathematics Education and Science

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work

