The total graph of a commutative ring

By David F. Anderson, Ayman Badawi. 2008

381 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/169a48bbd3512178e63ccc5a4b3ac01373961c18

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

On the Commuting Graph of Dihedral Group (2016, background): “We refer the readers to [2, 3] and references therein.”
THE GENERALIZED TOTAL GRAPH OF A COMMUTATIVE RING (2013, background): “When H = Z(R), we have that GTH(R) is the so-called total graph of R as introduced in [6] and denoted there by T (Γ(R)).”
On the Total Graph and Its Complement of a Commutative Ring (2013, background): “Badawi [2] introduced the total graph of a commutative ring.”
On the Dot Product Graph of a Commutative Ring (2015, neutral): “Recently, there has been considerable attention in the literature to associating graphs with algebraic structures (see [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [17], [18], [19], [20], [21], [23], [24], [25], and [26]).”
The Annihilating-Ideal Graph of Commutative Rings I (2008, background): “Recently Anderson and Badawi in [2] have introduced and investigated the total graph of R, denoted by T (Γ(R)).”
ON THE TOTAL GRAPH OF A COMMUTATIVE RING WITHOUT THE ZERO ELEMENT (2012, background): “The next two theorems summarize results about diam(Z(Γ(R))) (mentioned earlier from [5]) and diam(Z0(Γ(R))) when R is a finite commutative ring.”
Graphs Attached to Rings Revisited (2011, background): “1 ([4], Theorem 2.”
On the Genus of the Total Graph of a Commutative Ring (2013, background): “[4] introduced and studied the total graph of a commutative ring R.”
The total graph and regular graph of a commutative ring (2009, background): “The total graph of R denoted by T (Γ (R)) was introduced in [8], as the graph with all elements of R as vertices, and two distinct vertices x, y ∈ R are adjacent if and only if x + y ∈ Z(R).”