Diameter of the Zero Divisor Graph of Semiring of Matrices over Boolean Semiring
نویسنده
چکیده
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 and only if either xy = 0 or yx = 0. In this paper we study the zero divisor graph of the semiring of matrices Mn(B), (n > 1) over the Boolean semiring B. We investigate the properties of the right zero divisors and the left zero divisors of Mn(B) and then use these results to prove that the diameter of Γ(Mn(B)) is 3. Mathematics Subject Classification: 5C25
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