Involve: A Journal of Mathematics
- Volume 9, Number 3 (2016), 415-422.
Connectivity of the zero-divisor graph for finite rings
We study the vertex-connectivity and edge-connectivity of the zero-divisor graph associated to a finite commutative ring . We show that the edge-connectivity of always coincides with the minimum degree, and that vertex-connectivity also equals the minimum degree when is nonlocal. When 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.
Involve, Volume 9, Number 3 (2016), 415-422.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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