2006/06/20 by Lê Anh Vinh, Vinh, Le Anh
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.math/0606483
openalex publication_date 2006/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A divisor graph G is an ordered pair (V, E) where V ⊂ \mathbbmZ and for all u ≠ v ∈ V, u v ∈ E if and only if u | v or v | u. A graph which is isomorphic to a divisor graph is also called a divisor graph. In this note, we will prove that for any n \geqslant 1 and 0 \leqslant m \leqslant \binomn2 then there exists a divisor graph of order n and size m. We also present a simple proof of the characterization of divisor graphs which is due to Chartran, Muntean, Saenpholpant and Zhang.