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- W4287777450 abstract "The $k$-dimensional Weisfeiler-Leman algorithm ($k$-WL) is a very useful combinatorial tool in graph isomorphism testing. We address the applicability of $k$-WL to recognition of graph properties. Let $G$ be an input graph with $n$ vertices. We show that, if $n$ is prime, then vertex-transitivity of $G$ can be seen in a straightforward way from the output of 2-WL on $G$ and on the vertex-individualized copies of $G$. However, if $n$ is divisible by 16, then $k$-WL is unable to distinguish between vertex-transitive and non-vertex-transitive graphs with $n$ vertices as long as $k=o(sqrt n)$. Similar results are obtained for recognition of arc-transitivity." @default.
- W4287777450 created "2022-07-26" @default.
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- W4287777450 date "2020-05-18" @default.
- W4287777450 modified "2023-10-16" @default.
- W4287777450 title "The Weisfeiler-Leman Algorithm and Recognition of Graph Properties" @default.
- W4287777450 doi "https://doi.org/10.48550/arxiv.2005.08887" @default.
- W4287777450 hasPublicationYear "2020" @default.
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