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 ring with nonzero identity. The unit graph of R, denoted by G (R), has its set of
vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only …

Let S be a (multiplicative) commutative semigroup with 0. Associate to S a (simple) graph G
(S) with vertices the nonzero zero-divisors of S, and two distinct vertices x and y are adjacent …

Let R be a commutative ring with nonzero identity and, S⊆ R be a multiplicatively closed
subset. An ideal P of R with P∩ S=∅ is called an S-prime ideal if there exists an (fixed) s∈ S …

Let R be a commutative ring R with 1. In [PK Sharma, SM Bhatwadekar, A note on graphical
representation of rings, J. Algebra 176 (1995) 124–127], Sharma and Bhatwadekar defined …

Let (Γ (R)) c be 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 …

In this paper, a new kind of graph on a commutative ring R with identity, namely the co-
maximal ideal graph is defined and studied. We use to denote this graph, with its vertices the …

Let R be a commutative ring and Z (R) be its set of all zero-divisors. The total graph of R,
denoted by T Γ (R), is the undirected graph with vertex set R and two distinct vertices x and y …