English

On the PSU(4, 2)-invariant vertex-transitive strongly regular (216, 40, 4, 8) graph

Combinatorics 2019-07-31 v1

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 Γ\Gamma with parameters (216, 40, 4, 8) and proved that it is the unique PSU(4,2)-invariant vertex-transitive graph on 216 vertices. In this paper, using the geometry of the Hermitian surface of PG(3, 4), we provide a computer-free proof of the existence of the graph Γ\Gamma. The maximal cliques of Γ\Gamma are also determined.

Keywords

Cite

@article{arxiv.1907.12773,
  title  = {On the PSU(4, 2)-invariant vertex-transitive strongly regular (216, 40, 4, 8) graph},
  author = {Dean Crnković and Francesco Pavese and Andrea Švob},
  journal= {arXiv preprint arXiv:1907.12773},
  year   = {2019}
}