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arXiv · 2610.18463

The group generated by a graph's derangements

Mark Schachner·Gabe Udell
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Abstract

We introduce the leap group of a graph, the subgroup of the symmetric group on the vertex set generated by graph derangements. We summarize historical results on graph derangements, which we call hops, and prove additional existence and complexity results. The leap groups of various canonical graphs are computed, and their behavior under basic graph operations is analyzed. We offer partial results on which groups can appear as leap groups, and study hops and leaps for infinite and directed graphs.

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Mark Schachner, Gabe Udell. 2026-10-13. The group generated by a graph's derangements. https://arxiv.org/abs/2610.18463

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