Reliability analysis of twisted cubes

• DOI: 10.1016/j.tcs.2017.10.016
• Publication Date: 2017-10-24T17:30:29Z
• Authors: Litao Guo
• Keywords: 0102 computer and information sciences; 01 natural sciences

Abstract Connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model. Let G = ( V , E ) be a connected graph. A connected graph G is called supper-κ (resp. super-λ) if every minimum vertex cut (edge cut) of G is the set of neighbors of some vertex in G. Let F ⊆ V be a vertex set, F is called extra-cut, if G − F is not connected and each component of G − F has more than k vertices. The extraconnectivity κ k ( G ) is the cardinality of the minimum extra-cuts. A r-component cut of G is a set S of vertices, G − S has at least r components. r-component connectivity c κ r ( G ) of G is the size of the smallest r-component cut. The r-component edge connectivity c λ r ( G ) can be defined similarly. In this paper, we determine the r-component (edge) connectivity of twisted cubes T N n for small r. And we also prove other properties of T N n .