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.

For a commutative semigroup S with 0, the zero-divisor graph of S denoted by &Gamma(S) is the graph whose vertices are nonzero zero-divisor of S, and two vertices x, y are adjacent in case xy = 0 in S. In this paper we study median and center of this graph. Also we show that if Ass(S) has more than two elements, then the girth of &Gamma(S) is three.

a positive solution of the problem of the existence of nontrivial pairs of zero-divisors in group rings of free burnside groups of sufficiently large odd periods $n>10^{10}$ obtained previously by s. v. ivanov and r. mikhailov extended to all odd periods $ngeq 665$‎.

Let R be a commutative unital finite rings and Z(R) its set of zero divisors. The study automorphisms algebraic structures via divisor graphs is still an active area research. Perhaps, because the fact that have got real life application in capturing symmetries structures. In this study, such which product any four has been determined.