<![CDATA[Let G = (V, E) be a simple graph with n vertices, and let A be an abelian group of order n. Let f: V(G) → A be a bijection, and define the weight of a vertex x by w(x) = Σy ∈ N(x) f(y), where N(x) denotes the open neighborhood of x. We call f an A-distance magic labeling if all vertex weights are equal, and an A-distance antimagic labeling if the weights of distinct vertices are pairwise different. The prime graph of a commutative ring R is the simple graph with vertex set R in which two vertices x and y are adjacent if and only if xRy = {0}. In this paper, we investigate the existence of A-distance magic and A-distance antimagic labelings of the prime graph over the ring Zn for several values of n.]]>
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