The integer-antimagic spectra of Hamiltonian graphs
oleh: Ugur Odabasi, Dan Roberts, Richard M. Low
| Format: | Article |
|---|---|
| Diterbitkan: | Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2021-10-01 |
Deskripsi
<p class="p1"><span>Let </span><span class="math inline"><em>A</em></span><span> be a nontrivial abelian group. A connected simple graph </span><span class="math inline"><em>G</em> = (<em>V</em>, <em>E</em>)</span><span> is </span><span class="math inline"><em>A</em></span><span>-</span><em>antimagic</em><span>, if there exists an edge labeling </span><span class="math inline"><em>f</em> : <em>E</em>(<em>G</em>)→<em>A</em> ∖ {0<sub><em>A</em></sub>}</span><span> such that the induced vertex labeling </span><span class="math inline"><em>f</em><sup>+</sup>(<em>v</em>)=∑<sub>{<em>u</em>, <em>v</em>}∈<em>E</em>(<em>G</em>)</sub><em>f</em>({<em>u</em>, <em>v</em>})</span><span> is a one-to-one map. The </span><em>integer-antimagic spectrum</em><span> of a graph </span><span class="math inline"><em>G</em></span><span> is the set IAM </span><span class="math inline">(<em>G</em>)={<em>k</em> : <em>G</em> is ℤ<sub><em>k</em></sub>-antimagic and <em>k</em> ≥ 2}</span><span>. In this paper, we determine the integer-antimagic spectra for all Hamiltonian graphs.</span></p>