Graphs cospectral with NU(n + 1, q²), n ≠ 3

2020/12/19 by Ferdinand Ihringer, Francesco Pavese, Ihringer, Ferdinand +3 · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.2012.10651

arxiv created 2021/06/15 · arxiv updated 2021/06/16

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 P₁, P₂ are adjacent if the line joining P₁ and P₂ is tangent to H(n, q²). Then NU(n + 1, q²) is a strongly regular graph. In this paper we show that NU(n + 1, q²), n ≠ 3, is not determined by its spectrum.

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