The annihilator graph of a non-commutative semiring S denoted by AG(S) is the graph whose vertice set is the set of all nonzero zero-divisors of S denoted by Z(S)~* = Z(S){0} and two distinct vertices are adjacent if and only if either l · ann(xy) ≠ l · ann(x) ∪ l · ann(y), l · ann(yx) ≠ l · ann(x) ∪ l · ann(y), r · ann(xy) ≠ r · ann(x) ∪ r · ann(y), or r · ann(yx) ≠ r · ann(x) ∪ r · ann(y), where l · ann(a) = {s ∈ S|sa = 0} and r · ann(a) = {s ∈ S|as = 0} for a ∈ Z(S). In this paper, we show that AG(S) is connected with diameter at most two.
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机译：由AG表示的非换向性半型S的aniLipilator曲线图是其顶点集是由z（s）〜* = z（s） {0}表示的所有非零零除数集的图表 如果只有在L·ANN（XY）≠L·ANN（x），L·ANN（YX）≠L·ANN（x）∪l·安（ Y），R·ANN（XY）≠r·ANN（x）∪r·ANN（Y），或R·ANN（YX）≠R·ANN（x）∪r·安（y），其中l·安 （a）= {s∈s | sa = 0}和R·ANN（a）= {z的{s∈s | AS = 0}。 在本文中，我们表明AG（S）最多连接直径。
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