Note on Ideal Based Zero-Divisor Graph of a Commutative Ring

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(R/I ). 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
• 05c69
• 05c45
• 13a15