Vol. 11, No. 2, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 6, 901–1080
Issue 5, 721–899
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
Contacts
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Other MSP Journals
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
Abstract

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).

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

Communicated by Kenneth S. Berenhaut
Authors
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