Dan Roberts
Department of Mathematics, Illinois Wesleyan University, Bloomington, IL, 61701, USA

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The integer-antimagic spectra of Hamiltonian graphs Ugur Odabasi; Dan Roberts; Richard M. Low
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.2.5

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)→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.