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The $k$-dimensional Weisfeiler-Leman procedure ($k$-WL), which colors$k$-tuples of vertices in rounds based on the neighborhood structure in thegraph, has proven to be immensely fruitful in the algorithmic study of GraphIsomorphism. More generally, it is of fundamental importance in understandingand exploiting symmetries in graphs in various settings. Two graphs are$k$-WL-equivalent if the $k$-dimensional Weisfeiler-Leman procedure producesthe same final coloring on both graphs. 1-WL-equivalence is known as fractionalisomorphism 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 integralpacking numbers are typically NP-hard to compute, and we discuss applicabilityof $k$-WL-invariance for estimating the integrality gap of the LP relaxationprovided by their fractional counterparts.

On the Weisfeiler-Leman Dimension of Fractional Packing