For each commutative idealization ring L (+) G, we study the divisor graph of the zero-divisor graph L (+) G. For each commutative idealization ring L (+) G, we study the divisor graph of the zero-divisor graph L (+) G.

The aim of this article to follow the properties of the zero-divisor graph of special idealization ring. We study the wiener index of the zero-divisors graph of some special idealization ring R(+)M and find the clique number of the graph (R(+)M) is ω ((R(+)M))=|M|1, where R is an integral domain. We also discuss when the zero-divisors graph of some special idealization ring R(+)M are Hamiltonian graph.

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