Vertex and Edge Connectivity of the Zero Divisor graph \(\Gamma[\mathbb{Z}_n]\)

The Zero divisor Graph \(\Gamma[R]\) of a commutative ring \(R\) is a graph with vertex set being the set of non-zero zero divisors of \(R\) and there is an edge between two vertices if their product is zero. In this paper, we prove that the vertex, edge connectivity and the minimum degree of the ze...

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Bibliographic Details
Published in:Communications in Mathematics and Applications 2020-01, Vol.11 (2), p.253
Main Authors: B. Surendranath Reddy, Jain, Rupali S, Laxmikanth, N
Format: Article
Language:English
Subjects:
Apexes
Commutativity
Connectivity
Graph theory
Mathematics
Rings (mathematics)
Vertex sets
Online Access:Get full text
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Summary:The Zero divisor Graph \(\Gamma[R]\) of a commutative ring \(R\) is a graph with vertex set being the set of non-zero zero divisors of \(R\) and there is an edge between two vertices if their product is zero. In this paper, we prove that the vertex, edge connectivity and the minimum degree of the zero divisor graph \(\Gamma[\mathbb{Z}_n]\) for any natural number \(n\), are equal.
ISSN:0976-5905
0975-8607
DOI:10.26713/cma.v11i2.1319