Two-disjoint-cycle-cover bipancyclicity of bubble-sort star graphs.

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 |C1| = l and |C2| = |V(G)| -l, where |V(G)| denotes the number of vertices in G. In this paper, we explore some properties of the n-dimensional bubble-sort star graph BSn and prove that when n & GE; 4, for any even integer l satisfying 4 < l < n!/2, there exist two vertex-disjoint cycles C1 and C2 in BSn such that |C1| = l and |C2| = n! - l in BSn. This result supplements the Hamiltonicity and the bipancyclicity of BSn. & COPY; 2023 Elsevier B.V. All rights reserved.