Abstract: The parallel processing system is one of the research focuses on computer science. The properties of the network are very crucial because they determine the performance of the whole network. Many interconnection network topologies have been proposed. Hypercube topology has enjoyed popularity due to many of its attractive properties, including small diameter, strong connectivity and symmetry. But the hypercube is not the best topology on all aspects. Some variants of the hypercube have better properties than the hypercube. Among these variants the locally twisted cube has drawn a great deal of attention from the researchers. Its superior properties over the hypercube on diameter, Hamilton connectivity and some other properties have been proved. This paper gave a kind of connection-the hyper connection between the nodes of the hypercube and the nodes of the locally twisted cube. Thus, a new interconnection network called a LHL-cube was obtained by using this kind of connection. These properties were studied in this paper:vertex connectivity,link connectivity, Hamilton connectivity and diameter. The results show that the vertex connectivity and the link connectivity of then dimension LHL-cube are all n. Then it was proved that the n dimension LHL-cube is Hamilton connecuvmy and the upper bound diameter is [n/2]+3.

Key words: Hypercube, Locally twisted cube, Interconnection network, Connectivity, Hamilton property, Diameter