Face antimagic labelings of convex polytopes

Abstract

A connected plane graph G = (V, E, F) is said to be (a, d)-face antimagic if there exist positive integers a, d ∈ N and bijection g: E(G) → {1, 2, . . . , |E(G)|} such that the induced mapping ψ_g: F(G) → W is also a bijection, where W = {w(f): f ∈ F(G)} = {a, a + d, . . . , a + (|F(G)| - 1)d} is the set of weights of faces. The paper describes (a, d)-face antimagic labeling of a certain class of convex polytopes.