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

Authors

  • B. Surendranath Reddy School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded, Maharashtra
  • Rupali S. Jain School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded, Maharashtra
  • N. Laxmikanth School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded, Maharashtra

DOI:

https://doi.org/10.26713/cma.v11i2.1319

Keywords:

Zero divisor graph, Vertex connectivity, Edge connectivity, Minimum degree

Abstract

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.

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References

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B.S. Reddy, R.S. Jain and L. Nandala, Spectrum and Wiener index of the zero divisor graph (Gamma[mathbb{Z}n]), arXiv:1707.05083 [math.RA], URL https://arxiv.org/abs/1707.05083.

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Published

30-06-2020
CITATION

How to Cite

Reddy, B. S., Jain, R. S., & Laxmikanth, N. (2020). Vertex and Edge Connectivity of the Zero Divisor graph \(\Gamma[\mathbb{Z}_n]\). Communications in Mathematics and Applications, 11(2), 253–258. https://doi.org/10.26713/cma.v11i2.1319

Issue

Vol. 11 No. 2 (2020)

Section

Research Article

License

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