Abstract
Interconnection network is usually represented by a simple graph G. The structure connectivity κ(G;H) and substructure connectivity κs(G;H) are the new proposed indicators to measure network fault tolerance and reliability when the network fails with different structures. As a variant of the popular network hypercube, the crossed cube is also a famous interconnection network in parallel and distributed systems. In this paper, we establish the H-structure connectivity of the n-dimensional crossed cube when H∈{K1,1,K1,3,Pk,C4} and 3≤k≤n and H-substructure connectivity of the n-dimensional crossed cube when H∈{K1,1,K1,3,Pk,Cm}, 3≤k≤n and 4≤m≤n.
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