| K-connected networks are reliable because they can survive failure of any k-1 nodes. A network G is said to be (k,t)-connected if it is k-connected and the k-diameter of G is less than or equal to t. Let h(n,k,t) be the minimum number of edges G can have where G is (k,t)-connected and lV(G)l= n. We computer this number and look for optical networks G with lE(G)l= h(n,k,t), lV(G)l= n and G is (k,t)-connected. We pay special attention to the case k= 2. The class of (2,t)-connected networks have been used widely in the construction of fiber optical networks such as SONET/SDH and ATM networks. A (2,t)-connected network belongs to a larger class of networks called t-cyclic networks where each link belongs to a cycle of length less than or equal to t+1 Let f(n,t) be the minimum number of edges a t-cyclic network G with lV(G)l= n can have. We study f(n,t) and look for optimal networks G with lE(G)l= f(n,t), lV(G)l= n and G is t-cyclic. |