Vol. 8, No. 2, 2015

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Iteration digraphs of a linear function

Hannah Roberts

Vol. 8 (2015), No. 2, 221–232
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.

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