cliques in the extended zero-divisor graph of finite commutative rings

Let r be a finite commutative ring with or without unity and γe(r) be its extended zero-divisor graph with vertex set z∗(r) = z(r) {0} and two distinct vertices x, y are adjacent if and only if x.y = 0 or x + y ∈ z∗(r). in this paper, we characterize finite commutative rings whose extended zero-divisor graph have clique number 1 or 2. we completely characterize the rings of the form r ≅ r1 × r2, where r1 and r2 are local, having clique number 3, 4 or 5. further we determine the rings of the form r ≅ r1 × r2 × r3, where r1,r2 and r3 are local rings, to have clique number equal to six.