Let R be a commutative ring with nonzero identity, L_n(R) be the set of all lower triangular nxn matrices, and U be a triangular subset of R^n i.e. the product of any lower triangular matrix with the transpose of any element ...

Let R be a commutative ring with unity and R+, U and U∗ be the additive

group, multiplicative prime subset of R and U\\\\{0}. We denote by Cay(R)

the cayley graph Cay(R+,U^*). In this paper, we investigate ...

For a commutative ring R with non-zero identity, we denote the

set of non-zero element x in R with xR neq R by

W^*(R). So W^*(R) is the set of non-units of R. In this paper,

we introduced the ...

Let R be a Noetherian commutative ring. The regular digraph of ideals of

R introduced in [10] which denoted by

−−→

Γreg(R). The vertex set of

−−→

Γreg(R) is set of

nontrivial ideals ...

of

\\gama(R) is finite. Moreover, we study the independence number and

the girth of \\gama(R), and also we find all cases that \\gama(R) is bipartite....

Abstract. Let R be a ring, M be a left and right R-module. We associate a bipartite graph to R-module M of ring R, denoted by ΓR,M as undirected simple graph whose two parts of vertices are R\\CR(M) and M \\CM(R) and two ...

ABSTRACT: Let G be a finite group and N be a normal subgroup of G. We define an undirected simple graph N,G to

be a graph whose vertex set is all elements in G n ZN (G) and two vertices x and y are adjacent iff [x, ...

In this paper, using module endomorphisms, we extend the concept of the zero-divisor graph of a

ring to a module over an arbitrary commutative ring. The main aim of this article is studying the interplay of module ...

Let R be a commutative ring with nonzero identity and I be a proper ideal

of R. The annihilator graph of R with respect to I, which is denoted by AGI (R), is the

undirected graph with vertex-set V(AGI (R)) ...