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arXiv · 1711.01058

Divisor graph of complement of Gamma(R)

Ravindra Kumar·Om Prakash
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Abstract

Let overline{Γ(R)} be the complement of zero divisor graph of a finite commutative ring R. In this article, we have provided the answer of the question (ii) raised by Osba and Alkam in their paper and prove that overline{Γ(R)} is a divisor graph if R is a local ring. It is shown that when R is a product of two local rings, then overline{Γ(R)} is a divisor graph if one of them is an integral domain. Also, we prove that if cardinality of Ass(R) = 2, then overline{Γ(R)} is a divisor graph.

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Ravindra Kumar, Om Prakash. 2017-11-03. Divisor graph of complement of Gamma(R). https://arxiv.org/abs/1711.01058

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