Divisibility Graph

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An arrow is drawn from to
when (1)
is a factor of
and (2)
is prime. Consequently, there is a path of arrows from
to
if and only if
is a proper factor of
.
Contributed by: Don Goldberg (March 2011)
Based on a program by: Yifan Hu and Stephen Wolfram
Open content licensed under CC BY-NC-SA
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The relation divides
is a partial order: it is reflexive, antisymmetric, and transitive. These properties are expressed in the directed graphs generated here. Reflexivity: there is a path of (zero) arrows from each vertex to itself. Antisymmetry: if there is a path of arrows from
to
, there cannot be a path in the reverse direction. Transitivity: a path of arrows from
to
can be appended to a path of arrows from
to
to create a path from
to
.
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