  Like the RSK correspondence for symmetric groups, Garfinkle defined a domino
correspondence for type $\mathrm{B}$ and $\mathrm{D}$ Coxeter groups. Similar
to the Knuth relations, Taskin and Pietraho give the plactic relations for the
domino correspondence and Bonnaf\'e use them to classify the cells for type
$\mathrm{B}$ Coxeter groups. We give some further properties of the plactic
relations and use these relations to describe the bidirected edges and the
molecules of Gelfand $W$-graphs for type $\mathrm{B}$ and $\mathrm{D}$ Coxeter
groups.
