Vol. 11, No. 2, 2018

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Finding cycles in the $k$-th power digraphs over the integers modulo a prime

Greg Dresden and Wenda Tu

Vol. 11 (2018), No. 2, 181–194

For p prime and k 2, let us define Gp(k) to be the digraph whose set of vertices is {0,1,2,,p 1} such that there is a directed edge from a vertex a to a vertex b if ak b mod p. We find a new way to decide if there is a cycle of a given length in a given graph Gp(k).

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digraphs, cycles, graph theory, number theory
Mathematical Subject Classification 2010
Primary: 05C20
Secondary: 11R04
Received: 21 January 2014
Revised: 8 June 2017
Accepted: 21 June 2017
Published: 17 September 2017

Communicated by Kenneth S. Berenhaut
Greg Dresden
Department of Mathematics
Washington and Lee University
Lexington, VA
United States
Wenda Tu
Department of Statistics and Actuarial Science
University of Iowa
Iowa City, IA
United States