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تسجيل مستخدم جديدOn a new extension of the zero-divisor graph
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In this paper, we introduce a new graph whose vertices are the nonzero zero-divisors of commutative ring $R$ and for distincts elements $x$ and $y$ in the set $Z(R)^{star}$ of the nonzero zero-divisors of $R$, $x$ and $y$ are adjacent if and only if $xy=0$ or $x+yin Z(R)$. we present some properties and examples of this graph and we study his relation with the zero-divisor graph and with a subgraph of total graph of a commutative ring.
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We continue our study of the new extension of zero-divisor graph. We give a complete characterization for the possible diameters of $widetilde{Gamma}(R)$ and $widetilde{Gamma}(R[x_1,dots,x_n])$, we investigate the relation between the zero-divisor gr
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