Abstract
A bipartite graph G is two-disjoint-cycle-cover [r1, r2]-bipancyclic if for any even 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, where |V(G)| denotes the number of vertices in G. In this paper, we study the two-disjoint-cycle-cover bipancyclicity of the n-dimensional balanced hypercube BHn, which is a hypercube-variant network and is superior to hypercube due to having a smaller diameter. As a consequence, we show that BHn is two-disjoint-cycle-cover [4,22n−1]-bipancyclic for n ≥ 2.
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