On the Complement of the Intersection Graph of Zero-Divisors of the ring Zn Sajana Shaik*, Bharathi D., Srimitra K.K. Department of Mathematics, S.V. University, Tirupati, Andhra Pradesh, India-517502 *Corresponding Author E-mail: ssajana.maths@gmail.com
Online published on 12 June, 2018. 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. Top Keywords Intersection graph, Zero-divisors, Principal ideal, Connected graph, Eccentricity, Radius, Diameter. Top |
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