Iteration digraphs of a linear function

Roberts, Hannah

doi:10.2140/involve.2015.8.221

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Iteration digraphs of a linear function

Hannah Roberts

Vol. 8 (2015), No. 2, 221–232

DOI: 10.2140/involve.2015.8.221

Abstract

An iteration digraph $G (n)$ generated by the function $f (x) mod n$ is a digraph on the set of vertices $V = {0, 1, \dots, n - 1}$ with the directed edge set $E = {(v, f (v)) ∣ v \in V}$ . Focusing specifically on the function $f (x) = 10 x mod n$ , 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.

Keywords

digraph, cycle, congruence

Mathematical Subject Classification 2010

Primary: 05C20, 11A07

Milestones

Received: 5 November 2012

Revised: 4 March 2013

Accepted: 9 March 2013

Published: 3 March 2015

Communicated by Robert W. Robinson

Authors

Hannah Roberts
College of Wooster 91 Benton Street Austintown, OH 44515 United States

Vol. 8, No. 2, 2015