Graphs associated with orthogonal collections of k-planes over finite\n fields

2020/04/22 by Semin Yoo, Yoo, Semin
Computer Science · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2004.10742

openalex publication_date 2020/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study graphs coming from quadratic spaces over finite fields via\northogonality which generalize a recent result given by Bishnoi, Ihringer, and\nPepe (2019). More precisely, we study the graph \Γ ^square(n,k,q) as\nfollows: the vertex set is the set of k-dimensional quadratic subspaces of a\nfixed Lorentzian quadratic space\n( mathbbF_qⁿ,x₁²+\⋯+x_n-1²+\λ x_n²) which are\nisometrically isomorphic to x₁²+\⋯+x_k². Here \λ is a\nnonsquare in mathbbF_q, and two vertices x,y are adjacent if x\n\⊆ y^\⊥.\n

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