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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Science and Technology Indonesia BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika)
Krisnawati, Vira Hari
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Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Environmental Science Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Transportation

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On Group-Vertex-Magic Labeling of Simple Graphs Khuluq, Muhammad Husnul; Krisnawati, Vira Hari; Hidayat, Noor
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v8i2.23621

Abstract

Let A be an Abelian group with identity 0. The A-vertex-magic labeling of a graph G is a mapping from the set of vertices in G to A-{0} such that the sum of the labels of every open neighborhood vertex of v is equal, for every vertex v in G. In this article, we discuss group-vertex-magic labeling of some simple graphs by using the Abelian group Zk, with natural numbers k1. We investigated some classes of simple graphs are path graphs, complete graphs, cyclic graphs, and star graphs. The method we used in this article is literature study and then developing the properties of vertex-magic labeling of some simple graphs, that are path graphs, complete graphs, cyclic graphs, and star graphs. We obtain that complete graphs, cyclic graphs, and star graphs have Zk-vertex-magic labeling, while path graphs have vertex-magic labeling only for n=2,3.
Prime and Odd Prime Labelings on Cycle-Related Graphs Komarullah, Hafif; Hidayat, Noor; Krisnawati, Vira Hari; Wijaya, Kristiana
Science and Technology Indonesia Vol. 11 No. 2 (2026): April
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2026.11.2.551-558

Abstract

Graph labeling is the process of determining integer values for vertices, edges, or both, based on certain criteria. Let G be a simple graph with the finite vertex set V(G). Prime labeling of G is a bijection ⍺:V(G)→{1,2,…,|V(G)|} for which each pair of adjacent vertices exhibits relatively prime labels. This concept has been extended to odd prime labeling, defined as a bijection ⍺:V(G)→ {1,3,...,2|V(G)|-1} satisfying the condition that the labels assigned to adjacent vertices are relatively prime labels. A graph that displays a (odd) prime labeling is designated as a (odd) prime graph. A recent conjecture state that every prime graph is an odd prime graph. In the present study, we conduct an investigation concerning prime and odd prime labeling, focusing on a range of cycle-related graphs classes. Our methods include the axiomatic descriptive approach and pattern detection techniques. We show that volcano graphs, C_3 ⨀_(x_1 y_0 ) F_n, C_3⊚K ̅_n, tadpole graphs, palm trees, and C_l ⨀_(x_1 y_0 ) mP_(n+1) are all both prime and odd prime graphs.
Co-Authors Abdul Rouf Alghofari Ambarwati, Aditya Amigo, Royyan Fatimah, Farah Maulidya Hafif Komarullah Hidayat, Ardi Nur Karim, Corina Khuluq, Muhammad Husnul Kristiana Wijaya Musyarrofah, Ayunda Faizatul Noor Hidayat, Noor Sapitri, Ni Kadek Emik Sobri Abusini