## Involve: A Journal of Mathematics

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

### Iteration digraphs of a linear function

Hannah Roberts

#### 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
Revised: 4 March 2013
Accepted: 9 March 2013
First available in Project Euclid: 22 November 2017

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

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

#### References

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