Title of article :
The zero-divisor graph of a commutative ring without identity
Author/Authors :
Anderson, David F. Department of Mathematics - The University of Tennessee Knoxville, U.S.A , Weber, Darrin Department of Mathematics - The University of Evansville Evansville, U.S.A
Abstract :
Let R be a commutative ring. The zero-divisor graph of R is the
(simple) graph Γ(R) with vertices the nonzero zero-divisors of R, and two
distinct vertices x and y are adjacent if and only if xy = 0. In this article, we
investigate Γ(R) when R does not have an identity, and we determine all such
zero-divisor graphs with 14 or fewer vertices.
Keywords :
Zero-divisor graph , commutative ring without identity
