Edge-Magic Labelings of Generalized Petersen Graphs \(P(n, 2)\)

A graph \(G\) is called super-edge-magic if there exists a bijection \(f\) from \(V(G) \cup E(G)\) to \(\{1, 2, \ldots, |V(G)| + |E(G)|\}\) such that \(f(u) + f(v) + f(uv) = C\) is a constant for any \(uv \in E(G)\) and \(f(V(G)) = \{1, 2, \ldots, |V(G)|\}\). In this paper, we show that the generalized Petersen graph \(P(n, k)\) is super-edge-magic if \(n \geq 3\) is odd and \(k = 2\).