Abstract
In 2018 the first, Rukavina and the third author constructed with the aid of a computer the first example of a strongly regular graph \(\Gamma\) with parameters (216, 40, 4, 8) and proved that it is the unique \(\mathrm{PSU}(4,2)\)-invariant vertex-transitive graph on 216 vertices. In this paper, using the geometry of the Hermitian surface of \(\mathrm{PG}(3,4)\), we provide a computer-free proof of the existence of the graph \(\Gamma\). The maximal cliques of \(\Gamma\) are also determined.
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Acknowledgements
D. Crnković and A. Švob were supported by Croatian Science Foundation under the project 6732. The authors would like to thank the anonymous referees for helpful comments and suggestions.
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Crnković, D., Pavese, F. & Švob, A. On the \(\mathrm{PSU}(4,2)\)-Invariant Vertex-Transitive Strongly Regular (216, 40, 4, 8) Graph. Graphs and Combinatorics 36, 503–513 (2020). https://doi.org/10.1007/s00373-020-02132-5
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DOI: https://doi.org/10.1007/s00373-020-02132-5