Involve: A Journal of Mathematics

  • Involve
  • Volume 8, Number 2 (2015), 221-232.

Iteration digraphs of a linear function

Hannah Roberts

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An iteration digraph G(n) generated by the function f(x) mod n is a digraph on the set of vertices V = {0,1,,n 1} with the directed edge set E = {(v,f(v))v V }. Focusing specifically on the function f(x) = 10x mod n, we consider the structure of these graphs as it relates to the factors of n. The cycle lengths and number of cycles are determined for various sets of integers including powers of 2 and multiples of 3.

Article information

Involve, Volume 8, Number 2 (2015), 221-232.

Received: 5 November 2012
Revised: 4 March 2013
Accepted: 9 March 2013
First available in Project Euclid: 22 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C20: Directed graphs (digraphs), tournaments 11A07: Congruences; primitive roots; residue systems

digraph cycle congruence


Roberts, Hannah. Iteration digraphs of a linear function. Involve 8 (2015), no. 2, 221--232. doi:10.2140/involve.2015.8.221.

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