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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Journal of Mathematics Education and Science
Hardina Sandariria
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Education Mathematics

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Journal : Journal of Mathematics Education and Science

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Local Antimagic Edge Coloring Of Gear Graphs And Semi Parachute Graphs Dian Sri Rahmadani; Desi Febriani Putri; Wasono; Hardina Sandariria
Journal of Mathematics Education and Science Vol. 8 No. 2 (2025): Journal of Mathematics Education and Science
Publisher : Universitas Nahdlatul Ulama Sunan Giri Bojonegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32665/james.v8i2.4775

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.
Co-Authors Andrea Tri Dani Desi Febriani Putri Dian Sri Rahmadani Meirinda Fauziyah Wasono