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 $1,2,\dots ,|V(G)|+|E(G)|+|F(G)|$ so that the $s$-sided face weights form an arithmetic progression of difference $d$. This paper describes $d$-antimagie labelings for Möbius grids.