论文标题
符号内部产品图及其自动形态
Symplectic inner product graphs and their automorphisms
论文作者
论文摘要
在有限字段$ \ mathbb {f} _q $上引入了一个新图，称为Symbletic Inner产品图$ SPI \ big（2ν，Q \ big）$。我们表明，$ spi \ big（2ν，q \ big）$与直径$ 4 $相连，并且仅当$ s \ geq2 $和$ spi \ big（2ν，q \ big）$的自动形态组。在两个$ spi \ big（2ν，q \ big）$和两个$ spi \ big（2ν，q \ big）$的边缘的两个顶点和两个边缘在同一轨道上，在$ spi \ big（2ν，q \ big）的行动下，分别在相同的轨道上，有两个必要和足够的条件。
A new graph, called the symplectic inner product graph $Spi\big(2ν,q\big)$, over a finite field $\mathbb{F}_q$ is introduced. We show that $Spi\big(2ν,q\big)$ is connected with diameter $4$ if and only if $ν\geq2$ and the automorphism group of $Spi\big(2ν,q\big)$ is determined. Two necessary and sufficient conditions for two vertices of $Spi\big(2ν,q\big)$ and two edges of $Spi\big(2ν,q\big)$ respectively are in the same orbit under the action of the automorphism group of $Spi\big(2ν,q\big)$ are obtained.
