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Divisibility Graph


	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 Based on a program by: Yifan Hu and Stephen Wolfram

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

, there cannot be a path in the reverse direction. Transitivity: a path of arrows from

can be appended to a path of arrows from

to create a path from

Divisible (Wolfram MathWorld)

Partial Order (Wolfram MathWorld)

"Divisibility Graph" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/DivisibilityGraph/

Contributed by: Don Goldberg

Based on a program by: Yifan Hu and Stephen Wolfram

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