On the g-component connectivity of hypercube-like networks

Reliability evaluation of interconnection networks is of significant impor-tance to the design and maintenance of interconnection networks. The component connectivity is an important parameter for the reliability eval-uation of interconnection networks and is a generalization of the tradi-tional connectivity. Let g >= 0 be an integer and G be a connected graph. A g-component cut of G is a vertex set S such that G-S has at least g components. The g-component connectivity c kappa g(G) of G is the size of the smallest g-component cut. Determining the g-component connec-tivity is still an unsolved problem in many interconnection networks. In this paper, we prove the lower bound of the g-component connectivity of any n-dimensional hypercube-like networks. We also determine the g- component connectivity of varietal hypercubes and crossed cubes which are the members of hypercube-like networks. As a by-product, we charac-terize the optimal g-component cut under the condition that any two ver-tices have exactly two common neighbors if they have of any n-dimensional hypercube-like networks.