Nature of Graphs of Commutative Ring of Gaussian Integer modulo n under x3 - 1 mapping

Khalaf A. J. M., Nazeer S., Qayyum K., Cancan M.

Journal of Prime Research in Mathematics, vol.17, no.2, pp.58-72, 2021 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 2
  • Publication Date: 2021
  • Journal Name: Journal of Prime Research in Mathematics
  • Journal Indexes: Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.58-72
  • Keywords: In-degree, Regularity, Structure of digraph, Tree
  • Van Yüzüncü Yıl University Affiliated: Yes


© 2021. All Rights Reserved.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.