The integer-antimagic spectra of Hamiltonian graphs


ODABAŞI U., Roberts D., Low R. M.

ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS, vol.9, no.2, pp.301-308, 2021 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.5614/ejgta.2021.9.2.5
  • Title of Journal : ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS
  • Page Numbers: pp.301-308
  • Keywords: Hamiltonian graphs, graph labeling, group-antimagic labeling

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)P -> A/{0(A)} such that the induced vertex labeling f(+)(v) = Sigma({u,v}is an element of 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 Z(k)-antimagic and k >= 2}. In this paper, we determine the integer-antimagic spectra for all Hamiltonian graphs.