Divisor graphs have arbitrary order and size

dc.creatorVinh, Le Anh
dc.date2006-06-20
dc.date.accessioned2026-07-07T07:17:28Z
dc.date.available2026-07-07T07:17:28Z
dc.descriptionA 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.descriptionAWOCA 2006
dc.identifierhttps://arxiv.org/abs/math/0606483
dc.identifierhttp://arxiv.org/abs/math/0606483
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113953
dc.subjectCombinatorics
dc.titleDivisor graphs have arbitrary order and size
dc.typetext

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