论文标题
矢量空间上线性功能图的自动形态
Automorphisms of linear functional graphs over vector spaces
论文作者
论文摘要
令$ \ mathbb {f} _q $为有限字段，带有$ q $元素，$ n \ geq2 $正整数，$ \ mathbb {v} _0 $ a $ n $ n $ dimensional-dimensional-demensional-demensional-demensional-demensional-demensional-demensional-demensional-demensional-dimensional-demensional-demensional-demensional-demensional vector Space acy $ \ mathbb {f} $ \ mathbb {v} _0 $ to $ \ mathbb {f} _q $。令$ \ mathbb {v} = \ mathbb {v} _0 \ setMinus \ {0 \} $和$ \ mathbb {t} = \ m马理{t} _0 \ setMinus \ {0 \} $。 $ \ mathbb {V} _0 $由$ \ digamma（\ Mathbb {v}）$凹陷的\ emph {线性函数图}是一个无方向的二级图形图，其顶点set $ v $被将两个套件分为两个集合为$ v = \ mathbb {v = \ mathbb { $ v \ in \ mathbb {v} $和$ f \ in \ mathbb {t} $相邻，并且仅当$ f $ sends $ v $ sends $ v $ to $ \ mathbb {f} _q $（即$ f（v）= 0 $）。在本文中，该图的所有自动形态的结构均已表征和改造。也是自动形态组的基本数量 因为该图是确定的。
Let $\mathbb{F}_q$ be a finite field with $q$ elements, $n\geq2$ 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 $\mathbb{V}=\mathbb{V}_0\setminus\{0\}$ and $\mathbb{T}=\mathbb{T}_0\setminus\{0\}$. The \emph{linear functional graph} of $\mathbb{V}_0$ dented by $\digamma(\mathbb{V})$, 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. $f(v)=0$). In this paper, the structure of all automorphisms of this graph is characterized and formolized. Also the cardinal number of automorphisms group for this graph is determined.
