The maximal degree of a zero-divisor graph

The rings considered in this paper are finite commutative rings with identity, which are not fields. For any ring R which is not a field and which is not necessarily finite, we denote the set of all zero-divisors of R by Z(R) and Z(R)/{0} by Z(R). Let Gamma(R) denote the zero-divisor graph of R and for a finite ring R, let Delta(Gamma(R)) denote the maximum degree of Gamma(R). We denote {a is an element of Z(R)* vertical bar deg(Gamma) ((R)) (a) = Delta(Gamma(R))} by deg(Gamma(R)). The aim of this paper is to study some properties of M deg(Gamma(R)).