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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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