The integer-antimagic spectra of Hamiltonian graphs

Abstract

Let A be a nontrivial abelian group. A connected simple graph G = (V, E) is A-antimagic, if there exists an edge labeling f : E(G)P -> A/{0(A)} such that the induced vertex labeling f(+)(v) = Sigma({u,v}is an element of E(G)) f({u, v}) is a one-to-one map. The integer-antimagic spectrum of a graph G is the set IAM(G) = {k : G is Z(k)-antimagic and k >= 2}. In this paper, we determine the integer-antimagic spectra for all Hamiltonian graphs.