AUTHOR(S):

TITLE 
KEYWORDS Interconnection networks; Fault tolerance; rcomponent edge connectivity 
ABSTRACT Connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model. There are many kinds of connectivity to measure the fault tolerance and reliability of networks, such as classic connectivity, super connectivity, extraconnectivity. In this paper we focus on the number of components of graph which is called component connectivity. Let G = (V, E) be a connected graph. A rcomponent cut of G is a set of vertices whose deletion results in a graph with at least r components. rcomponent connectivity cκr (G) of G is the size of the smallest rcomponent cut. The rcomponent edge connectivity cλr (G) can be defined similarly. In this paper, we determine the rcomponent edge connectivity of hypercubes and folded hypercubes:(1) cλ2(Qn) = λ(Qn) = n for n ≥ 2. (2) cλ3(Qn) = 2n − 1 for n ≥ 2. (3) cλ4(Qn) = 3n − 2 for n ≥ 2. (4) cλ2(F Qn) = n + 1 for n ≥ 3. (5) cλ3(F Qn) = 2n + 1 for n ≥ 3. (6) cλ4(F Qn) = 3n + 1 for n ≥ 3. 
Cite this paper Litao Guo. (2017) Fault Tolerance of Hypercubes and Folded Hypercubes. International Journal of Mathematical and Computational Methods, 2, 7275 