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 $1,2,\dots ,m$ 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 $k=2,3,4$.