Let ${\mathbb{F}}_q$ be a finite field with q elements, $n\ge 2$ a positive integer, ${\mathbb{V}}_0$ a n-dimensional vector space over ${\mathbb{F}}_q$ and ${\mathbb{T}}_0$ the set of all linear functionals from ${\mathbb{V}}_0$ to ${\mathbb{F}}_q$. Let $\mathbb{V}={\mathbb{V}}_0\setminus \left\{0\right\}$ and $\mathbb{T}={\mathbb{T}}_0\setminus \left\{0\right\}$. The linear functional graph of ${\mathbb{V}}_0$ dented by $ϝ\left(\mathbb{V}\right)$, is an undirected bipartite graph, whose vertex set V is partitioned into two sets as $V=\mathbb{V}\cup \mathbb{T}$ and two vertices $v\in \mathbb{V}$ and $f\in \mathbb{T}$ are adjacent if and only if f sends v to the zero element of ${\mathbb{F}}_q$ (i.e. $f\left(v\right)=0$). In this paper, the structure of all automorphisms of this graph is characterized and formalized. Also the cardinal number of automorphisms group for this graph is determined.

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向量空间上线性泛函图的自同构

让${\mathbb{F}}_q$是一个有q个元素的有限域，$n\ge \mathrm{2个}$一个正整数，${\mathbb{V}}_0$一个n维向量空间${\mathbb{F}}_q$和${\mathbb{吨}}_0$来自的所有线性泛函的集合${\mathbb{V}}_0$到${\mathbb{F}}_q$. 让$\mathbb{V}={\mathbb{V}}_0\setminus \left\{0\right\}$和$\mathbb{吨}={\mathbb{吨}}_0\setminus \left\{0\right\}$. 的线性函数图${\mathbb{V}}_0$被削弱$\epsilon \left(\mathbb{V}\right)$, 是一个无向二分图，其顶点集V被划分为两个集合$V=\mathbb{V}\cup \mathbb{吨}$和两个顶点$v\in \mathbb{V}$和$F\in \mathbb{吨}$相邻当且仅当f将v发送到的零元素${\mathbb{F}}_q$（IE$F\left(v\right)=0$). 在本文中，对该图的所有自同构结构进行了表征和形式化。此图的自同构群的基数也已确定。