The Automorphism Group of NU(3,q²)

2021/12/01 by Federico Romaniello, Valentino Smaldore, Romaniello, Federico +1
Mathematics · #05C60 #05E30 #51E12 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C60 #msc:05E30 #msc:51E12

paper · pdf · doi:10.48550/arxiv.2112.00545

arxiv created 2022/03/03 · arxiv updated 2022/03/04

Abstract

Let H(n, q²) be a non-degenerate Hermitian variety of PG(n,q²), n ≥ 2. Let NU(n+1,q²) be the graph whose vertices are the points of PG(n,q²) ∖ H(n,q²) and two vertices u,~v are adjacent if the line joining u and v is tangent to H(n, q² ). Then NU(n + 1, q²) is a strongly regular graph. In this paper we show that the automorphism group of the graph NU(3,q²) is isomorphic either to PΓU(3,q), the automorphism group of the projective unitary group PGU(3,q), or to S₃ \wr S₄, according as q ≠ 2, or q=2.

Related

• Graphs cospectral with NU(n + 1, q²), n ≠ 3
• Quotients of the Hermitian curve from subgroups of rm PGU(3,q)\n without fixed points or triangles
• On a class of quasi-Hermitian surfaces in even characteristic
• A characterization of Hermitian varieties as codewords
• Characterization of non-singular hyperplanes of H(s,q²) in P G(s, q²)