Super Vertex (Edge)-Connectivity of Varietal Hypercube

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 Q(n), the varietal hypercube VQ(n) has better properties than Q(n) with the same number of edges and vertices. Wang and Xu have proved that VQ(n) is super vertex-connected for n & GE;1 and is also super edge-connected if n & NOTEQUAL;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 VQ(n).

Automated summary

The reliability measure of networks is crucial for network design and maintenance, and various quantitative indicators have been introduced based on connectivity. Super vertex edge-connectivity and cyclic edge-connectivity are important parameters to assess network robustness and have been extensively studied. This paper presents an alternative method to prove results related to the varietal hypercube and also determines its super restricted connectivity and cyclic edge-connectivity.