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Orthogonal Inner Product Graphs over Finite Fields of Odd Characteristic

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Listed:
  • Shouxiang Zhao
  • Hengbin Zhang
  • Jizhu Nan
  • Gaohua Tang
  • Xuanlong Ma

Abstract

Let Fq be a finite field of odd characteristic and 2ν+δ≥2 be an integer with δ=0,1, or 2. The orthogonal inner product graph Oi2ν+δ,q over Fq is defined, and a class of subgroup of the automorphism groups of Oi2ν+δ,q is determined. We show that Oi2ν+δ,q is a disconnected graph if 2ν+δ=2; otherwise, it is not. Moreover, we give necessary and sufficient conditions for two vertices and two edges of Oi2ν+δ,q, respectively, which are in the same orbit under the action of a subgroup of the automorphism group of Oi2ν+δ,q.

Suggested Citation

  • Shouxiang Zhao & Hengbin Zhang & Jizhu Nan & Gaohua Tang & Xuanlong Ma, 2023. "Orthogonal Inner Product Graphs over Finite Fields of Odd Characteristic," Journal of Mathematics, Hindawi, vol. 2023, pages 1-12, May.
    • Handle: RePEc:hin:jjmath:6811540
    DOI: 10.1155/2023/6811540
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