论文标题
在简单图的邻接矩阵的行中存在非零$（0,1）$ - 向量
Existence of a Non-Zero $(0,1)$-Vector in the Row Space of Adjacency Matrices of Simple Graphs
论文作者
论文摘要
我们在图$γ的相邻矩阵$ a（γ）$的行空间中寻找一个非零$（0，1）$ - 向量，提供$γ$至少具有一个优势。 Akbari，Cameron和Khosrovshahi猜想在行空间中存在非零$（0,1）$ - 向量的$ a（γ）$（γ）$（超过实际数字），这不会以$ a（γ）的行进行。在本文中，我们肯定地证明了直径为$ \ geq4的任何图的猜想。
We look for a non-zero $(0, 1)$-vector in the row space of the adjacency matrix $A(Γ)$ of a graph $Γ,$ provided $Γ$ has at least one edge. Akbari, Cameron, and Khosrovshahi conjectured that there exists a non-zero $(0,1)$-vector in the row space of $A(Γ)$ (over the real numbers) which does not occur as a row of $A(Γ).$ This conjecture can be easily verified for graphs having diameter is equal to $1$ (complete graphs). In this article, we affirmatively prove this conjecture for any graph whose diameter is $\geq 4.$ Furthermore, in the remaining two cases that is, for graphs with diameter is equal to $2$ or $3,$ we report some progress in support of the conjecture.
