论文标题
某些类别可分割的设计图的顶点连接性
The vertex connectivity of some classes of divisible design graphs
论文作者
论文摘要
如果可以将其顶点集分配为$ n $ $ n $的$ m $类别，则称为$ k $的图形，称为可划分的设计图，因此，来自同一类的两个不同的顶点恰好具有$λ_1$ common Neigner，而来自不同类别的两个顶点则完全具有$λ_2$ common neighbors。在本文中，我们发现了某些类别可分割的设计图的顶点连接性，尤其是我们介绍了可划分的设计图的示例，其顶点连接小于$ k $，其中$ k $是顶点的程度。我们还表明，通过2个功率，可划分的设计图可能小于$ k $的顶点连接。
A $k$-regular graph is called a divisible design graph if its vertex set can be partitioned into $m$ classes of size $n$, such that two distinct vertices from the same class have exactly $λ_1$ common neighbours, and two vertices from different classes have exactly $λ_2$ common neighbours. In this paper, we find the vertex connectivity of some classes of divisible design graphs, in particular, we present examples of divisible design graphs, whose vertex connectivity is less than $k$, where $k$ is the degree of a vertex. We also show that the vertex connectivity a divisible design graphs may be less than $k$ by any power of 2.
