Symplectic inner product graphs and their automorphisms
arXiv (Cornell University)(2022)
摘要
A new graph, called the symplectic inner product graph $Spi\big(2\nu,q\big)$, over a finite field $\mathbb{F}_q$ is introduced. We show that $Spi\big(2\nu,q\big)$ is connected with diameter $4$ if and only if $\nu\geq2$ and the automorphism group of $Spi\big(2\nu,q\big)$ is determined. Two necessary and sufficient conditions for two vertices of $Spi\big(2\nu,q\big)$ and two edges of $Spi\big(2\nu,q\big)$ respectively are in the same orbit under the action of the automorphism group of $Spi\big(2\nu,q\big)$ are obtained.
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关键词
symplectic inner product graphs,automorphisms
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