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Noor Hidayat, Noor
Fakultas Kesehatan Masyarakat, Universitas Ahmad Dahlan Yogyakarta
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Journal : Science and Technology Indonesia

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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 A.A. Ketut Agung Cahyawan W Abdul Rouf Abdul Rouf Alghofari Agus Suryanto Al-ghofari, Abdul Rouf Amandani, Dian Kartika Amigo, Royyan Damarian Prawira Hutama, Damarian Prawira Darmajid, Darmajid Dwi Mifta Mahanani, Dwi Mifta Edi Priyo Utomo Estri Laras Arumingtyas Exviani, Rina Fatimah, Farah Maulidya Fira Fitriah Fitriah, Zuraidah Hafif Komarullah Hidayahningrum, Syafitri Indah Yanti Joni Kusnadi Karim, Corina Khairi, Desfi Rahmatul Khuluq, Muhammad Husnul Krisnawati, Vira Hari Kristiana Wijaya Kurfia, Mustika Ana M.Pd S.T. S.Pd. I Gde Wawan Sudatha . Marjono Marjono Meilina, Kiki Amanda Eka Mohamad Muslikh Musyarrofah, Ayunda Faizatul Putra, M. Rafael Andika Rio Satriyantara shalsabilla, Az Zahra Sobri Abusini Syaiful Anam Wicaksono, Wildan Bagus Wijaya, Ongky Denny Wuryasari Muharini Kusumawinahyu