Thanks to Andreas' hint I found this slide show by Martin Fürer: Combinatorial Methods for the
Graph Isomorphism Problem. On slide 4 he treats vertex classification which is exactly similar in spirit to what I tried to sketch here (but expressed in three lines only):
Algorithm:
Start: Color the vertices by their degree.
Loop: Color the vertices by the multiset of colors of their neighbors.
Stop: When the color partition stabilizes.
So I am going to stop this thread here.