Involve: A Journal of Mathematics

  • Involve
  • Volume 9, Number 3 (2016), 415-422.

Connectivity of the zero-divisor graph for finite rings

Reza Akhtar and Lucas Lee

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Abstract

We study the vertex-connectivity and edge-connectivity of the zero-divisor graph ΓR associated to a finite commutative ring R. We show that the edge-connectivity of ΓR always coincides with the minimum degree, and that vertex-connectivity also equals the minimum degree when R is nonlocal. When R is local, we provide conditions for the equality of all three parameters to hold, give examples showing that the vertex-connectivity can be much smaller than minimum degree, and prove a general lower bound on the vertex-connectivity.

Article information

Source
Involve, Volume 9, Number 3 (2016), 415-422.

Dates
Received: 30 January 2015
Revised: 10 February 2015
Accepted: 4 March 2015
First available in Project Euclid: 22 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511371022

Digital Object Identifier
doi:10.2140/involve.2016.9.415

Mathematical Reviews number (MathSciNet)
MR3509335

Zentralblatt MATH identifier
1338.05114

Subjects
Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 13A99: None of the above, but in this section

Keywords
zero-divisor graph connectivity finite ring

Citation

Akhtar, Reza; Lee, Lucas. Connectivity of the zero-divisor graph for finite rings. Involve 9 (2016), no. 3, 415--422. doi:10.2140/involve.2016.9.415. https://projecteuclid.org/euclid.involve/1511371022


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