The cycle-structure connectivity of crossed cubes

Abstract

Crossed cube is a kind of network structure as a basis for distributed memory parallel computer architecture. Connectivity plays an important role in measuring the fault-tolerance of an interconnection network. As a generalization, Lin et al. [6] introduced the concept of structure connectivity in 2016. For connected graphs G and T, the T-structure connectivity κ(G;T) of G is the minimum cardinality of a set of subgraphs F of G that each member is isomorphic to T so that G−F is a disconnected or a trivial graph. In this paper, we study cycle-structure connectivity of n-dimensional crossed cubes CQn. We show that κ(CQn;C2k−1)=⌈nk−1⌉ for 4⩽k⩽n and κ(CQn;C2k)=⌊nk⌋+1 for even k with 4⩽k⩽n. Furthermore, we also obtain that κ(CQn;C6)=⌊n4⌋+⌈n−3⌊n4⌋2⌉ for n⩾4.