In recent years, graph theory has been used as a tool to study rings in the form of several different graphs, many of which are based on the zero divisor structure of the ring. We define here the Groebner zero divisor graph of a ring to try to harness the best possible graphical representation of a ring. This paper lays the foundation for the theory of monomial zero divisor graphs and the extension of them to a more general form, the Groebner zero divisor graph. We will study the relationships between the algebraic properties of a ring, and the graph theoretic properties of the Grobner zero divisor graph of that ring.
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