An upper bound for the crossing number of bubble-sort graph Bn

Symmetric graphs, such as the n-dimensional Boolean hypercube Qn, and the cube-connected cycles, have been widely used as processor or communication interconnection networks. For designing, analyzing and improving such networks, Akers and Krishnamurthy proposed a formal grouptheoretic model in [1]. Based on the model, the n-dimensional bubble-sort graph is proposed as one of those classes of networks that have better performance, as measured by diameter, connectivity, fault tolerance, etc, than the popular Qn. Thus, it has drawn a great deal of attention of research (see [2, 4, 9]).