Let M be an R-module. We associate an undirected graph Γ (M) to M in which nonzero
elements x and y of M are adjacent provided that xf (y)= 0 or yg (x)= 0 for some nonzero R …

Let R be a commutative ring with identity and M an R-module. In this paper, we associate a
graph to M, say Γ (M), such that when M= R, Γ (M) is exactly the classic zero-divisor graph …

In this article, we give several generalizations of the concept of zero-divisor elements in a
commutative ring with identity to modules. Then, for each 𝑅-module 𝑀, we associate three …

Let R be a commutative ring with identity, I its proper ideal and M be a unitary R-module. In
this paper, we introduce and study a kind of graph structure of an R-module M with respect …

For a commutative ring 𝑅 with identity, the ideal-based zero-divisor graph, denoted by Γ𝐼
(𝑅), is the graph whose vertices are 𝑥∊ 𝑅\𝐼| 𝑥𝑦∊ 𝐼 for some 𝑦∊ 𝑅\𝐼, and two distinct …

Let R be a commutative ring with unity. The cozero-divisor graph of R denoted by Γ′(R) is a
graph with the vertex set W*(R), where W*(R) is the set of all non-zero and non-unit …

The zero-divisor graph of a ring R is defined as the directed graph Γ (R) that its vertices are
all non-zero zero-divisors of R in which for any two distinct vertices x and y, x→ y is an edge …

For any commutative ring R that is not a domain, there is a zero-divisor graph, denoted Γ (R),
in which the vertices are the nonzero zero-divisors of R and two distinct vertices x and y are …

Zero-divisor graphs of amalgamated duplication of a ring along an ideal - ScienceDirect Skip
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Let R be a commutative ring and Γ (R) be its zero-divisor graph. In this paper it is shown that
for any finite commutative ring R, the edge chromatic number of Γ (R) is equal to the …