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All Journal Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika
Lase, Dermawan
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Mathematics

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Modular Irregular Labeling on Firecrackers Graphs Lase, Dermawan; Hinding, Nurdin; Amir, Amir Kamal
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 6 No. 1 (2023): Volume 6 Nomor 1 tahun 2023
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v6i1.2188

Abstract

Let G= (V, E) be a graph order n and an edge labeling ψ: E→{1,2,…,k}. Edge k labeling ψ is to be modular irregular -k labeling if exist a bijective map σ: V→Zn with σ(x)= ∑yϵv ψ(xy)(mod n). The modular irregularity strength of G (ms(G))is a minimum positive integer k such that G have a modular irregular labeling. If the modular irregularity strength is none, then it is defined ms(G) = ∞. Investigating the firecrackers graph (Fn,2), we find irregularity strength of firecrackers graph s(Fn,2), which is also the lower bound for modular irregularity strength, and then we construct a modular irregular labeling and find modular irregularity strength of firecrackers graph ms(Fn,2). The result shows its irregularity strength and modular irregularity strength are equal.
Modular Irregular Labeling on Firecrackers Graphs Lase, Dermawan; Hinding, Nurdin; Amir, Amir Kamal
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 6 No. 1 (2023): Inovasi Teknologi, Psikologi Belajar, dan Adaptasi Pembelajaran Matematika di E
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v6i1.2188

Abstract

Let G= (V, E) be a graph order n and an edge labeling ψ: E→{1,2,…,k}. Edge k labeling ψ is to be modular irregular -k labeling if exist a bijective map σ: V→Zn with σ(x)= ∑yϵv ψ(xy)(mod n). The modular irregularity strength of G (ms(G))is a minimum positive integer k such that G have a modular irregular labeling. If the modular irregularity strength is none, then it is defined ms(G) = ∞. Investigating the firecrackers graph (Fn,2), we find irregularity strength of firecrackers graph s(Fn,2), which is also the lower bound for modular irregularity strength, and then we construct a modular irregular labeling and find modular irregularity strength of firecrackers graph ms(Fn,2). The result shows its irregularity strength and modular irregularity strength are equal.
Co-Authors Amir Kamal Amir Hinding, Nurdin