Zero-divisor graphs in commutative rings Page 1 Zero-divisor graphs in commutative rings
David F. Anderson, Michael C. Axtell, and Joe A. Stickles, Jr. Abstract This article surveys the …

Let G be a non-abelian group and let Z (G) be the center of G. Associate a graph ΓG (called
non-commuting graph of G) with G as follows: Take G\Z (G) as the vertices of ΓG and join two …

In this book, we introduce several graphical representations of a ring. In the past three
decades, graphs constructed from algebraic structures have been studied extensively by …

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 …

Let R be a commutative ring with nonzero identity, Z (R) be its set of zero-divisors, and if a∈
Z (R), then let ann R (a)={d∈ R| da= 0}. The annihilator graph of R is the (undirected) graph …

Let R be a commutative ring. The total graph of R, denoted by T (Γ (R)) is a graph with all
elements of R as vertices, and two distinct vertices x, y∈ R, are adjacent if and only if x+ y∈ …

In a manner analogous to the commutative case, the zero-divisor graph of a non-
commutative ring R can be defined as the directed graph Γ (R) that its vertices are all non …

Full article: A Zero Divisor Graph Determined by Equivalence Classes of Zero Divisors Skip
to Main Content Taylor and Francis Online homepage Taylor and Francis Online homepage …

This paper answers the question of Anderson, Frazier, Lauve, and Livingston: for which finite
commutative rings R is the zero-divisor graph Γ (R) planar? We build upon and extend work …

Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted
by, is a graph with vertices in, which is the set of all non-zero and non-unit elements of R …