Antimagic Labelings of Cycle Powers

Abstract

An antimagic labeling of a graph with \(n\) vertices and \(m\) edges is a bijection from the set of edges to the integers \(1, 2, \ldots, m\) such that all \(n\) vertex sums are pairwise distinct. For a cycle \(C_n\) of length \(n\), the \(k\)-th power of \(C_n\), denoted by \(C_n^k\), is the supergraph formed by adding an edge between all pairs of vertices of \(C_n\) with distance at most \(k\). Antimagic labelings for \(C_n^k\) are given where \(k = 2, 3, 4\).