  The $k$-dimensional Weisfeiler-Leman procedure ($k$-WL), which colors
$k$-tuples of vertices in rounds based on the neighborhood structure in the
graph, has proven to be immensely fruitful in the algorithmic study of Graph
Isomorphism. More generally, it is of fundamental importance in understanding
and exploiting symmetries in graphs in various settings. Two graphs are
$k$-WL-equivalent if the $k$-dimensional Weisfeiler-Leman procedure produces
the same final coloring on both graphs. 1-WL-equivalence is known as fractional
isomorphism of graphs, and the $k$-WL-equivalence relation becomes finer as $k$
increases.
  We investigate to what extent standard graph parameters are preserved by
$k$-WL-equivalence, focusing on fractional graph packing numbers. The integral
packing numbers are typically NP-hard to compute, and we discuss applicability
of $k$-WL-invariance for estimating the integrality gap of the LP relaxation
provided by their fractional counterparts.
