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 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. The maximal cliques of Γ are also determined.
On the PSU (4 , 2) -Invariant Vertex-Transitive Strongly Regular (216, 40, 4, 8) Graph / Crnkovic, Dean; Pavese, Francesco; Svob, Andrea. - In: GRAPHS AND COMBINATORICS. - ISSN 0911-0119. - STAMPA. - 36:3(2020), pp. 503-513. [10.1007/s00373-020-02132-5]
On the PSU (4 , 2) -Invariant Vertex-Transitive Strongly Regular (216, 40, 4, 8) Graph
Pavese, Francesco
;
2020
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 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. The maximal cliques of Γ are also determined.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
