Diameter of the zero divisor graph of semiringof matrices over Boolean semiring

摘要

Let S be a semiring and let Z(S)? be its set of nonzero zero divisors.We denote the zero divisor graph of S by Γ(S) whose vertex set is Z(S)?and there is an edge between the vertices x and y (x 6= y) in Γ(S) if andonly if either xy = 0 or yx = 0. In this paper we study the zero divisorgraph of the semiring of matrices Mn(B), (n > 1) over the Booleansemiring B. We investigate the properties of the right zero divisors andthe left zero divisors of Mn(B) and then use these results to prove thatthe diameter of Γ(Mn(B)) is 3.