Divisor graphs have arbitrary order and size
| dc.creator | Vinh, Le Anh | |
| dc.date | 2006-06-20 | |
| dc.date.accessioned | 2026-07-07T07:17:28Z | |
| dc.date.available | 2026-07-07T07:17:28Z | |
| dc.description | A divisor graph $G$ is an ordered pair $(V, E)$ where $V \subset \mathbbm{Z}$ and for all $u \neq v \in V$, $u v \in E$ if and only if $u \mid v$ or $v \mid u$. 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 $0 \leqslant m \leqslant \binom{n}{2}$ 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. | |
| dc.description | AWOCA 2006 | |
| dc.identifier | https://arxiv.org/abs/math/0606483 | |
| dc.identifier | http://arxiv.org/abs/math/0606483 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113953 | |
| dc.subject | Combinatorics | |
| dc.title | Divisor graphs have arbitrary order and size | |
| dc.type | text |