Super Edge-Magic Labelings of Generalized Petersen Graphs \(P(n, 3)\)

Abstract

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 \(f(u) + f(v) + f(uv) = k\) is a constant for any \(uv \in E(G)\) and \(f(V(G)) = \{1,2,\ldots,|V(G)|\}\). Yasuhiro Fukuchi proved that the generalized Petersen graph \(P(n, 2)\) is super edge-magic for odd \(n \geq 3\). In this paper, we show that the generalized Petersen graph \(P(n,3)\) is super edge-magic for odd \(n \geq 5\).