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 …

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 …

In this paper we continue our study of annihilating-ideal graph of commutative rings, that
was introduced in (The annihilating-ideal graph of commutative rings I, to appear in J …

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∈ …

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 …

Let R be a ring with unity and I (R)* be the set of all nontrivial left ideals of R. The intersection
graph of ideals of R, denoted by G (R), is a graph with the vertex set I (R)* and two distinct …

Zero-divisor graphs of finite commutative rings: a survey Page 1 Surveys in Mathematics and
its Applications ISSN 1842-6298 (electronic), 1843-7265 (print) Volume 15 (2020), 371 – 397 …

Let R be a ring with non-zero identity and U (R) be the group of units of R. The unit graph of
R, denoted by G (R), is a graph defined on the elements of R, and two distinct vertices r and …

In this paper we study zero-divisor graphs of rings and semirings. We show that all zero-
divisor graphs of (possibly noncommutative) semirings are connected and have diameter …

In this paper we investigate the structure of quaternion rings over the finite field Zp. This work
is based on M. Aristidou and A. Demetre's paper,“A Note on Quaternion Rings over Zp”, who …