The integer-antimagic spectra of Hamiltonian graphs

Ugur Odabasi (Department of Engineering Sciences, Istanbul University-Cerrahpasa, Istanbul, 34320, Turkey)
Dan Roberts (Department of Mathematics, Illinois Wesleyan University, Bloomington, IL, 61701, USA)
Richard M. Low (Department of Mathematics and Statistics, San Jose State University, San Jose, CA, 95192, USA)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications

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.