The bubble sort graph Bn has as its vertices the n! permutations u = u1u2 . . . un of the integers 1, 2, . . . , n, with u adjacent to the n-1 vertices u1u2 . . . ui−1ui+1ui . . . un for 1 ≤ i ≤ n − 1. Fig. 1 shows the bubble sort graphs for n = 3 and n = 4.