In section 35.1 of the book "Linear algebraic groups" by Humphreys, it is stated that the quasi-split but not split semisimple groups can only arise when the root system admits a nontrivial graph automorphism.

Moreover, it seems that the relative root system in this case is obtained by adjoining the vertices of Dynkin diagram which are sent to each other by the graph automorphism.

Also in the wikipedia page on quasi-split groups, it is stated that a quasi-split groups over a field correspond to actions of the absolute Galois group on a Dynkin diagram.

In both, there is no reference about this statement. In what paper can I find some theory about this?