… Let R be a commutative ring with Nil(R) its ideal of nilpotent elements, Z(R) its set of zero-…
and investigate the total graph of R, denoted by T (Γ (R)). It is the (undirected) graph with all …

… Total graph and regular graph are Hamiltonian Now, we want to determine when the total
graph and the regular graph of a finite commutative ring … is a finite commutative ring and Z ( R ) …

… ring R. In this paper, we introduce the generalized total graph of R, denoted by GTH(R), as
the (simple) graph … When H = Z(R), we have that GTH(R) is the so-called total graph of R as …

… , 32, 33, 35, 37]; and several variants of the total graph have been studied in [1, 8, 9, 14, 16,
… on the total graph of a commutative ring and its related graphs. Let G be a (simple) graph. …

… The study on total graphs has been initiated by DF Anderson and A. Badawi [Citation2]. In …
all commutative rings whose total graph (or its complement) is in some known class of graphs. …

… , we characterize all isomorphism classes of finite commutative rings whose total graph has
… genus of the total graph and characterize all commutative rings whose total graph has genus …

… number of the total graph of an Artin ring equals the … total graph of some classes of rings,
now we propose a conjecture for the domination number of the total graph of a commutative ring…

… In Section 2, we study the structure of total graphs when the set of zero divisor of R is an
ideal. In … of total graphs of commutative rings, when the set of zero divisor of rings is an ideal. …

… Let R be a commutative ring and I its proper ideal, let S(I) be the set of … total graph of a
commutative ring R with respect to proper ideal I, denoted by T(ΓI (R)). It is the (undirected) graph …

… total graphs of a commutative ring R in this paper, except TΓ(M) whose vertex set is M, have
the same vertex set R. In each graph, … The study of each such graph breaks naturally into two …