… a ring with identity and (R) ∼= (Mn(F)), then R ∼= Mn(F). We also prove that if R and S are
two finite commutative rings … use (R) for this graph and call it co-maximal graph. In Section 3, …

… , y ∈ m, for some maximal ideal m of R. We call this graph as a Maximal graph associated
with R. It is easy to see that every maximal ideal in R forms a maximally complete subgraph of …

… kind of graph on a commutative ring R with identity, namely the co-maximal ideal graph is …
In this paper, we define a new kind of graph structure on a commutative ring R. The vertices …

… commutative ring and Γ (R) be its zero-divisor graph. In this paper it is shown that for any finite
commutative ring … to the maximum degree of Γ (R), unless Γ (R) is a complete graph of odd …

… the ring-theoretic properties of a commutative ring and the graph-theory properties of its
zero-divisor graph. … Also, when R has no strongly isolated maximal ideal, every cycle in Γ(R) has …

… We also write Mn(R) and Max(R), for the set of n × n matrices over the ring R and the set of
all maximal left ideals of R, respectively. In this paper Fq denotes the field with q elements. An …

… of a graph G and Max(R) is the set of maximal ideals of R. Moreover, we find all finite rings R
… In this paper, R will denote a commutative ring with 1. If S is a subset of R, we denote S − {0} …

… graph theoretic problem that seems rather unmanageable when restricted to methods from
graph theory is solved using a straightforward ring … the graph G(R) on a commutative ring R …

… Since the induced subgraph of C(R) on maximal ideals of R is a complete graph and C(R)
dose not contain K∞, we conclude that |Max(R)| < ∞. Assume that n is the largest number …

… the maximal graph of a commutative ring with identity R whose vertices are elements of R.
Two distinct vertices a and b are adjacent if and only if Ra + Rb ̸= R or there exists a maximal …