论文标题
左矩阵环上左左矩阵的左态性图
Automorphisms of left Ideal relation graph over full matrix ring
论文作者
论文摘要
环$ r $上的左理想关系图，由$ \ toceRightArrow {γ_{γ_{l-i}}}（r）$表示，是一个定向图表，其顶点套件是$ r $的所有元素，并且从$ x $中有一个指向$ x $的元素，只有$ x $的$ y $，只有$ y $ y，只有$ y $ y的$ x $ proffy of $ x $ porter y porthy y porthy porthy porter y porthy porthy porthy porthy of x $ x $ x $ x $ [x] $ y $。在本文中，表征了$ \ overrightArrow {γ_{l-i}}（r）$的自动形态，其中$ r $是所有$ n \ times n $矩阵的戒指，上面是有限的字段$ f_q $。无方向的左图图，由$γ_{l-i}（m_n（f_q））$表示，是一个简单的图形，其顶点是$ r $的所有元素和两个不同的顶点$ x，y $在且仅当$ [x] \ subset [y] $ [y] $或$ [y] $或$ [y] $或$ [y] $ [y] $ [y] $ [y] $ supstect and Ifned and y necadect in ackeent。研究了$γ_{l-i}（m_n（f_q））$的各种图理论属性，包括连接性，周围，集团数量等。
The left-ideal relation graph on a ring $R$, denoted by $\overrightarrow{Γ_{l-i}}(R)$, is a directed graph whose vertex set is all the elements of $R$ and there is a directed edge from $x$ to a distinct $y$ if and only if the left ideal generated by $x$, written as $[x]$, is properly contained in the left ideal generated by $y$. In this paper, the automorphisms of $\overrightarrow{Γ_{l-i}}(R)$ are characterized, where $R$ is the ring of all $n \times n$ matrices over a finite field $F_q$. The undirected left relation graph, denoted by $Γ_{l-i}(M_n(F_q))$, is the simple graph whose vertices are all the elements of $R$ and two distinct vertices $x, y$ are adjacent if and only if either $[x] \subset [y]$ or $[y] \subset [x]$ is considered. Various graph theoretic properties of $Γ_{l-i}(M_n(F_q))$ including connectedness, girth, clique number, etc. are studied.
