Two-disjoint-cycle-cover pancyclicity of data center networks

A graph G is two-disjoint-cycle-cover [r1,r2]-pancyclic if for any integer ℓ satisfying r1≤ℓ≤r2, there exist two vertex-disjoint cycles C1 and C2 in G such that |V(C1)|=ℓ and |V(C2)|=|V(G)|−ℓ. The k-dimensional data center network DCell with n port switches and order tk,n, denoted by Dk,n, plays an important role in big data cloud computing. In this paper, we study the structural properties of Dk,n and show that Dk,n is two-disjoint-cycle-cover [3,⌊tk,n2⌋]-pancyclic for n≥7 and n+k≥11, that is, for any integer ℓ satisfying 3≤ℓ≤⌊tk,n2⌋, there exist two vertex-disjoint cycles C1 and C2 such that |V(C1)|=ℓ and |V(C2)|=tk,n−ℓ in Dk,n. This paper generalizes the results about the Hamiltonicity in (Wang et al., 2015 [25]) and the pancyclicity in (Hao and Tian, 2021 [11]).