Nature of Graphs of Commutative Ring of Gaussian Integer Modulo N Under X3 - 1 Mapping
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Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abdus Salam School of mathematical Sciences
Abstract
The aim of the present paper is to observe the structures of digraphs derived from the mappings f1: Zn[i] Zn[i] defined by f1 (x) = x3 — 1 whose vertex is Zn[i] = {a + bi: a, b (Formula presented) Zn} and for which there is a directed edge from x (Formula presented) Zn[i] to y (Formula presented) Zn[i] if and only if x3 — 1 = y (mod n). In this article, we investigated the structure of digraph. The in-degree of 1 and 0 in D1(n) are established where D1(n) is digraph obtained. Some regularity conditions of D1(n) are also discussed. For certain values of n, the simple conditions for the number of components and length of cycles is obtained. © 2021. All Rights Reserved.
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Keywords
In-Degree, Regularity, Structure Of Digraph, Tree
Turkish CoHE Thesis Center URL
WoS Q
N/A
Scopus Q
Q2
Source
Journal of Prime Research in Mathematics
Volume
17
Issue
2
Start Page
58
End Page
72