The Zero Divisor Graph of the Ring Zqp.

Abstract

In this paper we construct a star zero divisor graph from the zero divisor graph of the ring Zqp. The star zero divisor graph is obtained by removing some vertices from the zero divisor graph Γ(Zqp), in different ways , but the best way to get star zero divisor graph SΓ(Zqp) is by removing an odd number of zero divisors. Finally the crossing number, the girth and the diameter of this graph is also determined.

Keywords

• Commutative rings
• zero divisor graphs
• star zero divisor graph
• crossing number
• girth of the graph