Involve: A Journal of Mathematics

  • Involve
  • Volume 11, Number 2 (2018), 181-194.

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

Greg Dresden and Wenda Tu

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Abstract

For p prime and k2, let us define Gp(k) to be the digraph whose set of vertices is {0,1,2,,p1} such that there is a directed edge from a vertex a to a vertex b if akb modp. We find a new way to decide if there is a cycle of a given length in a given graph Gp(k).

Article information

Source
Involve, Volume 11, Number 2 (2018), 181-194.

Dates
Received: 21 January 2014
Revised: 8 June 2017
Accepted: 21 June 2017
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513775055

Digital Object Identifier
doi:10.2140/involve.2018.11.181

Mathematical Reviews number (MathSciNet)
MR3733950

Zentralblatt MATH identifier
06817013

Subjects
Primary: 05C20: Directed graphs (digraphs), tournaments
Secondary: 11R04: Algebraic numbers; rings of algebraic integers

Keywords
digraphs cycles graph theory number theory

Citation

Dresden, Greg; Tu, Wenda. Finding cycles in the $k$-th power digraphs over the integers modulo a prime. Involve 11 (2018), no. 2, 181--194. doi:10.2140/involve.2018.11.181. https://projecteuclid.org/euclid.involve/1513775055


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