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On the automorphism group of a putative Conway 99-graph
Cesarz, Patrick G.1; Woldar, Andrew J.2
1 University of Wyoming Dept. of Mathematics & Statistics 1000 E. University Ave. Laramie, WY 82071 (USA)
2 Villanova University Dept. of Mathematics & Statistics 800 E. Lancaster Ave. Villanova, PA (USA)
Algebraic Combinatorics, Volume 8 (2025) no. 2, pp. 379-398.

Let $\Gamma $ be a Conway 99-graph, that is, a strongly regular graph with parameters $(99,14,1,2)$. Existence of such a graph remains an elusive open problem, however various authors have made significant contributions by analyzing the structure of the automorphism group $G={\rm Aut}(\Gamma )$. In this paper we duplicate many results of our predecessors (e.g. Behbahani & Lam, Crnković & Maksimović), but crucially, we accomplish this without the aid of a computer. Specifically, we give computer-free proofs that divisibility of $|G|$ by $2$ implies $|G|$ divides $6$ while divisibility of $|G|$ by $7$ implies $G \cong \mathbb{Z}_7$.

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Accepted:
Published online:
DOI: 10.5802/alco.418
Classification: 05E18, 05C25, 58D19
Keywords: Conway $99$-graph, strongly regular graph, automorphism group, orbit partition, orbit valencies

Cesarz, Patrick G. 1; Woldar, Andrew J. 2

1 University of Wyoming Dept. of Mathematics & Statistics 1000 E. University Ave. Laramie, WY 82071 (USA)
2 Villanova University Dept. of Mathematics & Statistics 800 E. Lancaster Ave. Villanova, PA (USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Cesarz, Patrick G.; Woldar, Andrew J. On the automorphism group of a putative Conway 99-graph. Algebraic Combinatorics, Volume 8 (2025) no. 2, pp. 379-398. doi : 10.5802/alco.418. https://alco.centre-mersenne.org/articles/10.5802/alco.418/

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