The number of non-sources in the directed graphs of rings of integers modulo a prime power

Document Type

Article

Publication Date

1-1-2021

Abstract

For a prime p and positive integer n, let Zp(n) and Psi(Z(p)(n)) denote the ring of integers modulo p(n) and the directed graph associated with the ring Zp(n), respectively. In this paper, we obtain an explicit formula for determining the number of non-sources in the directed graph Psi(Zp(n)). This formula may then be used to determine the number of non-sources in the directed graph Psi(Z(m)) where m is a positive integer.

Keywords

Finite ring, Directed graph, Graph associated with a ring, Source of graph

Divisions

MathematicalSciences

Funders

Universiti Malaya (FG038-17AFR)

Publication Title

Ars Combinatoria

Volume

154

Publisher

Charles Babbage Research Centre

Publisher Location

PO BOX 272 ST NORBERT POSTAL STATION, WINNIPEG, MB R3T 2N2, CANADA

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