Abstract: Complete-transposition networks are a class of important Cayley graphs in networks design. The k-restricted vertex(edge)-connectivity of a graph G is the minimum cardinality of a set of vertices (edges) in G whose removal results in disconnected and each component has at least k vertices, denoted by \kappa_{k}(\lambda_{k}). The k-restricted vertex(edge)-connectivity is one of the most parameters to evaluate the reliability of a network, it is also a refined measure of the fault tolerance of the graph. In general, the larger the k-restricted vertex(edge)-connectivity of a network, the more reliable the network. The paper proves that 2-restricted vertex(edge)-connectivity and 3-restricted vertex(edge)-connectivity of complete-transposition networks, that is, when n\geq4, \kappa_{2}(CT_{n})=n(n-1)-2, \kappa_{3}(CT_{n})=\frac{3n(n-1)}{2}-6, when n\geq3, \lambda_{2}(CT_{n})=n(n-1)-2, \lambda_{3}(CT_{n})=\frac{3n(n-1)}{2}-4.

Key words: interconnection networks, Cayley graphs, complete-transposition networks, restricted vertex-connectivity, restricted edge-connectivity