Muhammad Husnul Khuluq, Vira Hari Krisnawati, N. Hidayat
Let G = (V(G),E(G)) be a graph, (A,+) be an Abelian group with identity 0A, and (R, +, ·) be a ring. The A-vertex-magic labeling of G is a mapping from V (G) to A− {0A} such that the total labels of every adjacent vertex with u are equal for every u in V (G). The prime graph over R, denoted by PG(R), is a graph with V (PG(R)) = R such that uv is an edge if and only if uRv = {0R} or vRu = {0R}, for every vertex u ≠ v. In this article, we discuss the Zk-vertex-magic labeling of the prime graph over the ring Zn. We study some literature to develop the properties of Zk-vertex-magic labeling of PG(R). We investigate some classes of prime graphs over ring Zn for n = p, n = p2, and n = pq, with p ≠ q primes. © 2025 University of Guilan.
Department of Mathematics, Faculty of Mathematics and Sciences, University of Brawijaya, Malang, Indonesia
