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


Affiliations
1 Department of Mathematics, S.V. University, Tirupati, A.P., -517502, India
     

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For the ring of integers modulo 𝑛, we study the complement of the intersection graph of zero-divisors is denoted by 𝐺𝑍′ (𝑍𝑛)Μ… 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 𝐺𝑍′ (𝑍𝑛)Μ…. Also, we investigate the connectedness and further calculate the radius and diameter of the graph 𝐺𝑍′ (𝑍𝑛)Μ… for all characterizations of 𝑛.

Keywords

Intersection Graph, Zero-Divisors, Principal Ideal, Connected Graph, Eccentricity, Radius, Diameter.
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  • On the Complement of the Intersection Graph of Zero-Divisors of the Ring Zn

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Authors

Shaik Sajana
Department of Mathematics, S.V. University, Tirupati, A.P., -517502, India
D. Bharathi
Department of Mathematics, S.V. University, Tirupati, A.P., -517502, India
K. K. Srimitra
Department of Mathematics, S.V. University, Tirupati, A.P., -517502, India

Abstract


For the ring of integers modulo 𝑛, we study the complement of the intersection graph of zero-divisors is denoted by 𝐺𝑍′ (𝑍𝑛)Μ… 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 𝐺𝑍′ (𝑍𝑛)Μ…. Also, we investigate the connectedness and further calculate the radius and diameter of the graph 𝐺𝑍′ (𝑍𝑛)Μ… for all characterizations of 𝑛.

Keywords


Intersection Graph, Zero-Divisors, Principal Ideal, Connected Graph, Eccentricity, Radius, Diameter.

References