Median and Center of Zero-Divisor Graph of Commutative Semigroups

For a commutative semigroup S with 0, the zero-divisor graph of S denoted by (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 ??(S) is three.