Some properties of the zero divisor graph of a commutative ring
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2014, Vol 34, Issue 2
Abstract
Let Γ(R) be the zero divisor graph for a commutative ring with identity. The k-domination number and the 2-packing number of Γ(R), where R is an Artinian ring, are computed. k-dominating sets and 2-packing sets for the zero divisor graph of the ring of Gaussian integers modulo n, Γ(Zn[i]), are constructed. The center, the median, the core, as well as the automorphism group of Γ(Zn[i]) are determined. Perfect zero divisor graphs Γ(R) are investigated. Keywords: automorphism group of a graph, center of a graph, core of a graph, k-domination number, Gaussian integers modulo n, median of a graph, 2-packing, perfect graph, and zero divisor graph. 2010 Mathematics Subject Classification: 05C25, 13Axx
Authors and Affiliations
Khalida Nazzal, Manal Ghanem
Keywords
Related Articles
- EP ID EP165232
- DOI -
- Views 53
- Downloads 0
ON THE AUTOTOPISM GROUP OF THE CORDERO-FIGUEROA SEMIFIELD OF ORDER 3^6
In [5] M. Biliotti, V. Jha and N. Johnson were able to completely determine the autotopism group of a generalized twisted field as a subgroup of ΓL(K) × ΓL(K), where K = GF(p^n) and ΓL(K) is the group of nonsingular semi...
On balanced order relations and the normal hull of completely simple semirings
In [1] the authors proved that a semiring S is a completely simple semiring if and only if S is isomorphic to a Rees matrix semiring over a skew-ring R with sandwich matrix P and index sets I and Λ which are bands under...
CODES OVER HYPERFIELDS
In this paper, we define linear codes and cyclic codes over a finite Krasner hyperfield and we characterize these codes by their generator matrices and parity check matrices. We also demonstrate that codes over finite Kr...
HOLOMORPH OF GENERALIZED BOL LOOPS II
The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the...
ALL MAXIMAL COMPLETELY REGULAR SUBMONOIDS OF HypG(2)
In this paper we consider mappings σ which map the binary operation symbol f to the term σ(f) which do not necessarily preserve the arity. These mapping are called generalized hypersubstitutions of type τ = (2) and we de...