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A new infinite family of covers of complete graphs that admit a half-transitive action of a Suzuki simple group
Abstract
We construct a new infinite family of antipodal 2(q−1)-covers of complete graphs Kq2+1 of diameter $3$, where q=22e+1≥ 8, admitting a half-transitive action of the Suzuki simple group Sz(q). We further show that each constructed cover admits an involutory automorphism interchanging the two Sz(q)-orbits on arcs, which yields that its full automorphism group is arc-transitive.
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BibTeX
@misc{tsiovkina2026infinite,
title = {{A new infinite family of covers of complete graphs that admit a half-transitive action of a Suzuki simple group}},
author = {Ludmila Yu. Tsiovkina},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36165},
eprint = {2610.36165},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36165},
}
RIS
TY - UNPB
TI - A new infinite family of covers of complete graphs that admit a half-transitive action of a Suzuki simple group
AU - Ludmila Yu. Tsiovkina
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36165
UR - https://arxiv.org/abs/2610.36165
AB - We construct a new infinite family of antipodal 2(q−1)-covers of complete graphs K_q^2+1 of diameter $3$, where q=2^2e+1≥ 8, admitting a half-transitive action of the Suzuki simple group Sz(q). We further show that each constructed cover admits an involutory automorphism interchanging the two Sz(q)-orbits on arcs, which yields that its full automorphism group is arc-transitive.
ER -