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Properties of the `k-equivalent' graph families constructed in Cai, Fürer and Immerman, and Evdokimov and Ponomarenko are analysed relative the the recursive k-dim WL method. An extension to the recursive k-dim WL method is presented that is shown to efficiently characterise all such types of `counterexample' graphs, under certain assumptions. These assumptions are shown to hold in all known cases.
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B. L. Douglas (2011) studied this question.