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All Journal Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika
Indi Izzah Makhfudloh
Department of Mathematics Education, University of Jember, East Java 68121, Indonesia
Religion Education Mathematics Physics Other

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Local edge (a, d) –antimagic coloring on sunflower, umbrella graph and its application Robiatul Adawiyah; Indi Izzah Makhfudloh; Rafiantika Megahnia Prihandini
Alifmatika (Jurnal pendidikan dan pembelajaran Matematika) Vol 5 No 1 (2023): Alifmatika - June
Publisher : Fakultas Tarbiyah Universitas Ibrahimy

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35316/alifmatika.2023.v5i1.70-81

Abstract

Suppose a graph G = (V, E) is a simple, connected and finite graph with vertex set V(G) and an edge set E(G). The local edge antimagic coloring is a combination of local antimagic labelling and edge coloring. A mapping f∶ V (G)→ {1, 2, ..., |V (G)|} is called local edge antimagic coloring if every two incident edges e_1and e_2, then the edge weights of e_1and e_2 maynot be the same, w(e_1) ≠ w(e_2), with e = uv ∈ G, w(e) = f(u)+ f(v) with the rule that the edges e are colored according to their weights, w_e. Local edge antimagic coloring has developed into local (a,d)-antimagic coloring. Local antimagic coloring is called local (a,d)-antimagic coloring if the set of edge weights forms an arithmetic sequence with a as an initial value and d as a difference value. The graphs used in this study are sunflower graphs and umbrella graphs. This research will also discuss one of the applications of local edge (a,d)-antimagic coloring, namely the design of the Sidoarjo line batik motif. The result show that χ_le(3,1) (Sf_n) = 3n and χ_le(3n/2,1) (U_(m,n) ) = m+1 . The local (a,d)-antimagic coloring is formed into a batik motif design with characteristics from the Sidoarjo region.
Co-Authors Rafiantika Megahnia Prihandini Robiatul Adawiyah