Local Antimagic Edge Coloring Of Gear Graphs And Semi Parachute Graphs

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Authors

  • Dian Sri Rahmadani Universitas Mulawarman
  • Desi Febriani Putri Universitas Mulawarman
  • Wasono Universitas Mulawarman
  • Hardina Sandariria Universitas Mulawarman

DOI:

https://doi.org/10.32665/james.v8i2.4775

Keywords:

Chromatic, Edge Coloring, Gear, Local Antimagic, Semi Parachute

Abstract

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.

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Published

2025-09-08

How to Cite

[1]
Dian Sri Rahmadani, Desi Febriani Putri, Wasono, and Hardina Sandariria, “Local Antimagic Edge Coloring Of Gear Graphs And Semi Parachute Graphs”, JaMES, vol. 8, no. 2, pp. 123–132, Sep. 2025.
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