The integer-antimagic spectra of Hamiltonian graphs - Ugur Odabasi; Dan Roberts; Richard M. Low (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2021)
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)→A ∖ 0A such that the induced vertex labeling f+(v)=∑u, v∈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 ℤk-antimagic and k ≥ 2. In this paper, we determine the integer-antimagic spectra for all Hamiltonian graphs.