Two-disjoint-cycle-cover vertex bipancyclicity of bubble-sort star graph

A bipartite graph <i>G</i> is two-disjoint-cycle-cover (TDCC for short)[c1,c2] -bipancy-clic if <i>G</i> possesses two vertex-disjoint cycles (TVDC for short) C1 and C2 such that c1≤l1≤c2, l1+l2=|V(G)|, where li is the length of Ci for i∈{1,2}. A bipartite graph <i>G</i> is TDCC vertex [c1,c2]-bipancyclic by adding the condition that for any two vertices v1 and v2, v1∈V(C1) and v2∈V(C2). Let BSn denote the <i>n</i>-dimensional bubble-sort star graph, which is a widely studied interconnection network and possesses many favourable properties. In this paper, we demonstrate that BSn is TDCC vertex [4,n!2]-bipancyclic and TDCC [4,n!2]-bipancyclic, where n≥4. Since |V(BSn)|=n! and BSn is a bipartite graph, this result is optimal.