It is welI known ([1], p. 28) that all $n!$ arrangements of $n$ symbols can be ordered without repetition so that each can be obtained from the previous one by a single transposition.
See also C. Savage, "A survey of combinatorial Gray codes", SIAM Rev., 39, 605 (1997):
Examples of combinatorial Gray codes include (1) listing all permutations of $1 \dots n$ so that consecutive permutations differ only by the swap of one pair of adjacent elements [Joh63, Tro62]