The integer-antimagic spectra of a disjoint union of Hamiltonian graphs

Abstract

Let A be a nontrivial abelian group. A simple graph G = (V, E) is A-antimagic, if there exists an edge labeling f : E(G) -> A {0} such that the induced vertex labeling f(+) (v) = Sigma(uv is an element of E(G) )f(uv) 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 a disjoint union of Hamiltonian graphs.