Some graph theoretical properties over zero-divisor graphs of special finite commutative rings

Let R be a commutative ring with identity and let ?(R) be the set of zero-divisors of R. It has been widely studied the notion of the zero-divisor graph of R which is defined by ?T(R) = ?(R) \{0} such that the 'distinct vertices x and y are adjacent if and only if xy = 0. As main results of this paper, by considering R = ? q×? q for different primes p and q, we prove some graph theoretical properties over ?(? p × ? q) which are the generalizations of the results in [12].