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The group generated by a graph's derangements
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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BibTeX
@misc{schachner2026group,
title = {{The group generated by a graph's derangements}},
author = {Mark Schachner and Gabe Udell},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18463},
eprint = {2610.18463},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18463},
}
RIS
TY - UNPB
TI - The group generated by a graph's derangements
AU - Mark Schachner
AU - Gabe Udell
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18463
UR - https://arxiv.org/abs/2610.18463
AB - 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.
ER -