Bisection width of transposition graphs

Abstract

We prove lower and upper bounds on bisection width of transposition graphs. This class of graphs contains several frequently studied interconnection networks including star graphs and hypercubes. In particular, we prove that the bisection width of the complete transposition graph is of order Θ( n. n!) which solves the open problem (R) 3.356 of Leighton's book [10] and determine an asymptotically exact value of bisection width of the star graph. The results have applications to VLSI layouts, cutwidth and crossing numbers of transposition graphs. We also study bandwidth of these graphs.