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arXiv · 1707.01267

The Weisfeiler-Leman algorithm and the diameter of Schreier graphs

Daniele Dona
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Abstract

We prove that the number of iterations taken by the Weisfeiler-Leman algorithm for configurations coming from Schreier graphs is closely linked to the diameter of the graphs themselves: an upper bound is found for general Schreier graphs, and a lower bound holds for particular cases, such as for Schreier graphs with $G=\mbox{SL}_{n}({\mathbb F}_{q})$ ($q>2$) acting on $k$-tuples of vectors in ${\mathbb F}_{q}^{n}$; moreover, an exact expression is found in the case of Cayley graphs.

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Daniele Dona. 2018-09-05. The Weisfeiler-Leman algorithm and the diameter of Schreier graphs. https://doi.org/10.4171/ggd%2F521

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