Super-connectivity and super-edge-connectivity for some interconnection networks

摘要

Let G=(V,E) be a k-regular graph with connectivity κ and edge connectivity λ. G is maximum connected if κ=k, and G is maximum edge connected if λ=k. Moreover, G is super-connected if it is a complete graph, or it is maximum connected and every minimum vertex cut is {x|(v,x)∈E} for some vertex v∈V; and G is super-edge-connected if it is maximum edge connected and every minimum edge disconnecting set is {(v,x)|(v,x)∈E} for some vertex v∈V. In this paper, we present three schemes for constructing graphs that are super-connected and super-edge-connected. Applying these construction schemes, we can easily discuss the super-connected property and the super-edge-connected property of hypercubes, twisted cubes, crossed cubes, möbius cubes, split-stars, and recursive circulant graphs.