We determine the number of edges of the zero-divisor graph of the direct product of finitely many finite non-commutative rings or semigoups.

In this paper, we examine the linear codes with respect to Hamming metric from incidence matrices of zero-divisor graphs vertex set consisting all non-zero zero- divisors ring ℤn and two distinct vertices being adjacent if their product is zero over ℤn. The main parameters are obtained.

Let R be a commutative ring and let ? Z n the zero divisor graph of id="M2"> R , whose vertices are nonzero divisors id="M3"> such that two id="M4"> u , v adjacen...

Let R be a commutative ring with nonzero identity and Z(R) its set of zero-divisors. The new extension the zero-divisor graph $$\widetilde{\Gamma }(R)$$ vertices $$Z(R)^{\star }$$ , two distinct x y are adjacent if only $$xy=0$$ or $$x+y\in Z(R)$$ . In this article, we study, in general case, For any R, provide sufficient necessary conditions for }(R[x_1,\dots x_n])$$ to complete. At last, pres...