$k$-iso-regular graphs are the graphs in which every $k$-tuple has a same number of neighbors. The $k$-dimensional Weisfeiler Lehman fails on $k$-iso-regular regular graphs. $k$ is a constant here, definitely if $k = O(n)$ then $k$-dimensional Weisfeiler Lehman will work correctly.

Suppose I bound the maximum degree of the input graph to three, then also there are graphs on which $k$-dimensional Weisfeiler Lehman fails. So one possible way to deal this situation is individualization along with $k$-dimensional Weisfeiler Lehman.

Question : Is there any known claim on the size of individualization set for $k$-iso-regular graphs ( degree at max three )?

I tried to search on google scholar, but did not get anything specific.