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arXiv · 2309.16590

Vertex-primitive digraphs with large fixity

Marco Barbieri·Primož Potočnik
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Abstract

The relative fixity of a digraph $Γ$ is defined as the ratio between the largest number of vertices fixed by a nontrivial automorphism of $Γ$ and the number of vertices of $Γ$. We characterize the vertex-primitive digraphs whose relative fixity is at least $1/3$, and we show that there are only finitely many vertex-primitive digraphs of bounded out-valency and relative fixity exceeding a positive constant.

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Marco Barbieri, Primož Potočnik. 2023-09-28. Vertex-primitive digraphs with large fixity. https://doi.org/10.1007/s10231-024-01447-x

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