Research Journal of Science and Technology

  • Year: 2017
  • Volume: 9
  • Issue: 3

On the Complement of the Intersection Graph of Zero-Divisors of the ring Zn

Department of Mathematics, S.V. University, Tirupati, Andhra Pradesh, India-517502

Abstract

For the ring of integers modulo n, we study the complement of the intersection graph of zero-divisors is denoted by and is defined as a simple undirected graph whose vertices are the set of all nonzero zero-divisors of the ring Zn and in which two distinct vertices are joined by an edge if and only if their corresponding principal ideals have zero intersection. We determine the necessary and sufficient condition for adjacency of vertices in the graph . Also, we investigate the connectedness and further calculate the radius and diameter of the graph for all characterizations of n.

Keywords

Intersection graph, Zero-divisors, Principal ideal, Connected graph, Eccentricity, Radius, Diameter