Commutative Algebra

pp 39-54


On the Total Graph of a Ring and Its Related Graphs: A Survey

  • Ayman BadawiAffiliated withDepartment of Mathematics and Statistics, American University of Sharjah Email author 

* Final gross prices may vary according to local VAT.

Get Access


Let R be a (commutative) ring with nonzero identity and Z(R) be the set of all zero divisors of R. The total graph of R is the simple undirected graph T(Γ(R)) with vertices all elements of R, and two distinct vertices x and y are adjacent if and only if x + yZ(R). This type of graphs has been studied by many authors. In this paper, we state many of the main results on the total graph of a ring and its related graphs.


Total graph Zero divisors Diameter Girth Connected graph Genus Generalized total graph Dominating set Clique Chromatic number

MSC(2010) classification

13A15 13B99 05C99