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arXiv · 2205.10730

Orthogonal inner product graphs of odd characteristic and their automorphisms

Shouxiang Zhao·Hengbin Zhang·Jizhu Nan·Gaohua Tang
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Abstract

Let $\mathbb{F}_q$ be a finite field of odd characteristic and $2\nu+\delta\geq2$ an integer number with $\delta=0,1$ or $2$. The orthogonal inner product graph $Oi\big(2\nu+\delta,q\big)$ over $\mathbb{F}_q$ is defined and the automorphism groups of $Oi\big(2\nu+\delta,q\big)$ are determined. We show that $Oi\big(2\nu+\delta,q\big)$ is a disconnected graph if $2\nu+\delta=2$; otherwise it is not. Moreover, we have two necessary and sufficient conditions for two vertices of $Oi\big(2\nu+\delta,q\big)$ and two edges of $Oi\big(2\nu+\delta,q\big)$ respectively are in the same orbit under the action of the automorphism group of $Oi\big(2\nu+\delta,q\big).$

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Shouxiang Zhao, Hengbin Zhang, Jizhu Nan, Gaohua Tang. 2022-05-22. Orthogonal inner product graphs of odd characteristic and their automorphisms. https://arxiv.org/abs/2205.10730

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