Super Vertex (Edge)-Connectivity of Varietal Hypercube

Abstract

The reliability measure of networks is of significant importance to the design and maintenance of networks. Based on connectivity, many refined quantitative indicators for the reliability of network systems have been introduced. The super vertex edge-connectivity and cyclic edge-connectivity, as important parameters to evaluate the robustness of networks, are explored extensively. As a variant of the hypercube Qn, the varietal hypercube VQn has better properties than Qn with the same number of edges and vertices. Wang and Xu have proved that VQn is super vertex-connected for n≥1 and is also super edge-connected if n≠2. In this paper, we use another method to prove these results. Moreover, we also obtain the super restricted connectivity and the cyclic edge-connectivity of the varietal hypercube VQn.

Keywords

• reliability
• super vertex (edge)-connectivity
• cyclic edge-connectivity
• vertex-transitivity
• edge-transitivity
• varietal hypercube