# The total graph of a commutative ring

```@article{Anderson2008TheTG,
title={The total graph of a commutative ring},
author={David F. Anderson and Ayman Badawi},
journal={Journal of Algebra},
year={2008},
volume={320},
pages={2706-2719}
}```
• Published 1 October 2008
• Mathematics
• Journal of Algebra
273 Citations

### ON THE TOTAL GRAPH OF A COMMUTATIVE RING WITHOUT THE ZERO ELEMENT

• Mathematics
• 2012
Let R be a commutative ring with nonzero identity, and let Z(R) be its set of zero-divisors. The total graph of R is the (undirected) graph T(Γ(R)) with vertices all elements of R, and two distinct

### The total graph of a finite commutative ring

Let R be a commutative ring with Z(R) , its set of zero-divisors and Reg(R) , its set of regular elements. Total graph of R , denoted by T (Γ(R)) , is the graph with all elements of R as vertices,

### The Regular Graph of a Non-Commutative Ring

• Mathematics
Electron. Notes Discret. Math.
• 2014

### The regular graph of a commutative ring

• Mathematics
Period. Math. Hung.
• 2013
If R is a commutative Noetherian ring and 2 ∈ Z(R), then the chromatic number and the clique number of G(R) are the same and they are 2n, where n is the minimum number of prime ideals whose union is Z( R).

### When a total graph associated with a commutative ring is perfect?

• Mathematics
Publications de l'Institut Math?matique (Belgrade)
• 2020
Let R be a commutative ring with identity, and let Z(R) be the set of zero-divisors of R. The total graph of R is the graph T(?(R)) whose vertices are all elements of R, and two distinct vertices x

### Total Zero Divisor Graph of a Commutative Ring

• Mathematics
• 2012
ABSTRACT Let R be a commutative ring with Z(R), its set of zero divisors. The total zero divisor graph of R, denoted Z(Γ(R)) is the undirected (simple) graph with vertices Z(R)*=Z(R)-{0}, the set of

### Total Graphs of Idealization

• Mathematics
• 2014
Let R be a commutative ring with Z(R), its set of zero divisors. The total zero divisor graph of R, denoted Z(Γ(R)) is the undirected (simple) graph with vertices Z(R)=Z(R)-{0}, the set of nonzero

### The Girth of the Total Graph of ℤ n

• Mathematics
Proceedings of the 1st International Conference on Mathematics and Mathematics Education (ICMMEd 2020)
• 2021
Let R be a commutative ring with a non-zero identity, and Z(R) is a set of zero-divisors of R. The total graph of R, denoted TΓ(R), is an (undirected) graph with all elements R as vertices of TΓ(R)

### On the nilpotent graph of a ring

• Mathematics
Turkish Journal of Mathematics
• 2013
Let R be a ring with unity. The nilpotent graph of R , denoted by ΓN (R) , is a graph with vertex set ZN (R) ∗ = {0 � x ∈ R | xy ∈ N (R) for some 0 � y ∈ R} ; and two distinct vertices x and y are