Involve: A Journal of Mathematics

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

Iteration digraphs of a linear function

Hannah Roberts

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511370857

Digital Object Identifier
doi:10.2140/involve.2015.8.221

Mathematical Reviews number (MathSciNet)
MR3320855

Zentralblatt MATH identifier
1309.05086

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

Keywords
digraph cycle congruence

Citation

Roberts, Hannah. Iteration digraphs of a linear function. Involve 8 (2015), no. 2, 221--232. doi:10.2140/involve.2015.8.221. https://projecteuclid.org/euclid.involve/1511370857


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References

  • K. H. Rosen, Elementary number theory and its applications, 4th ed., Addison-Wesley, Reading, MA, 2000.
  • L. Somer and M. Křížek, “On a connection of number theory with graph theory”, Czechoslovak Math. J. 54(129):2 (2004), 465–485.
  • D. Wilson, “Divisibility by 7 is a walk on a graph”, 2009, hook http://blog.tanyakhovanova.com/?p=159 \posturlhook.