Divisor graphs have arbitrary order and size

Details Divisor graphs have arbitrary order and size Divisor graphs have arbitrary order and size

2006-06-20

arxiv.org/abs/math/0606483v1

Mathematics

Combinatorics

AWOCA 2006

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Divisor graphs have arbitrary order and size does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Divisor graphs have arbitrary order and size, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Divisor graphs have arbitrary order and size will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-40275