Hafif Komarullah, Noor Hidayat, Vira Hari Krisnawati, Kristiana Wijaya
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 α: 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 α: 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, C3 ⊙x1 y0 Fn, C3 ⊙¯Kn, tadpole graphs, palm trees, and Cl ⊙x1 y0 mPn+1 are all both prime and odd prime graphs. © 2026, Magister Program of Material Sciences, Graduate School of Sriwijaya University. All rights reserved.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Brawijaya, Malang, 65145, Indonesia; Department of Mathematics Education, Faculty of Education, Universitas Al Falah Assunniyyah, Jember, 68167, Indonesia; Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Jember, Jember, 68121, Indonesia
