A NOTE ON IDEAL BASED ZERO-DIVISOR GRAPH OF A COMMUTATIVE RING
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2017, Vol 37, Issue 2
Abstract
In this paper, we consider the ideal based zero divisor graph ΓI (R) of a commutative ring R. We discuss some graph theoretical properties of ΓI (R) in relation with zero divisor graph. We also relate certain parameters like vertex chromatic number, maximum degree and minimum degree for the graph ΓI (R) with that of Γ( RI). Further we determine a necessary and sufficient condition for the graph to be Eulerian and regular. Keywords: zero-divisor graph, chromatic number, ideal based zero divisor graph, clique number. 2010 Mathematics Subject Classification: 05C69, 05C45, 13A15.
Authors and Affiliations
A. Mallika, R. Kala, K. Selvakumar
Keywords
Related Articles
- EP ID EP304572
- DOI -
- Views 64
- Downloads 0
COMPLICATED BE-ALGEBRAS AND CHARACTERIZATIONS OF IDEALS
In this paper, using the notion of upper sets, we introduced the notions of complicated BE-Algebras and gave some related properties on complicated, self-distributive and commutative BE-algebras. In a self-distributive a...
ON L-FUZZY MULTIPLICATION MODULES
Let L be a complete lattice. In a manner analogous to a commutative ring, we introduce and investigate the L-fuzzy multiplication modules over a commutative ring with non-zero identity. The basic properties of the prime...
COMMUTATIVITY OF PRIME RINGS WITH SYMMETRIC BIDERIVATIONS
The present paper shows some results on the commutativity of R: Let R be a prime ring and for any nonzero ideal I of R, if R admits a biderivation B such that it satisfies any one of the following properties (i) B([x, y]...
IF-FILTERS OF PSEUDO-BL-ALGEBRAS
Characterizations of IF-filters of a pseudo-BL-algebra are established. Some related properties are investigated. The notation of prime IF- filters and a characterization of a pseudo-BL-chain are given. Homomorphisms of...
PSEUDO-BCH-ALGEBRAS
The notion of pseudo-BCH-algebras is introduced, and some of their properties are investigated. Conditions for a pseudo-BCH-algebra to be a pseudo-BCI-algebra are given. Ideals and minimal elements in pseudo-BCH algebras...