Codes in Star and Bubble-sort graphs

The objects under consideration are codes in Cayley graphs of the symmetric group, namely in Star and Bubble-sort graphs. The tables of optimal codes in the Star graphs S
5
and S
6
are presented. We suggest several infinite series of completely regular codes with covering radius 1 in the Bubble-sort graphs and enumerate the intersection arrays of these codes in the Star graphs $S_{5}, S_{6}$ and the Bubble-sort graphs B
4
and B
5
. For obtaining the results of the paper, binary linear programming was used in a combination with traditional techniques.