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) = ∑ uv∈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 Zk-antimagic and k ≥ 2}. In this paper, we determine the integer-antimagic spectra for a disjoint union of Hamiltonian graphs.