Antimagic labelings of Mobius grids

Abstract

A \(d\)-antimagic labeling of a plane graph \(G = (V, E, F)\) is a one-to-one mapping taking the vertices, edges, and faces onto the integers \(1, 2, \ldots, |V(G)| + |E(G)| + |F(G)|\) so that the \(s\)-sided face weights form an arithmetic progression of difference \(d\). This paper describes \(d\)-antimagie labelings for Möbius grids.