论文标题
在交叉点上的理想图表
On the intersection ideal graph of semigroups
论文作者
论文摘要
半群$ s $的交点理想图$γ（s）$是一个简单的无向图，其顶点都是$ s $的无平凡的左侧理想，而两个不同的左左理想$ i，j $仅在其交叉点不算时才相邻。在本文中，我们研究了$γ$的连接性。我们表明，如果连接$γ（s）$，则$ diam（γ（s））\ leq 2 $。此外，我们对半群进行了分类，使其相交图的直径为两个。还讨论了其他图形不变性，即完美，平面，周长，优势数，集团数，独立数等。最后，如果$ s $是$ n $ n $少的左左理想的联合，那么我们将获得$γ（S）$的自动形态组。
The intersection ideal graph $Γ(S)$ of a semigroup $S$ is a simple undirected graph whose vertices are all nontrivial left ideals of $S$ and two distinct left ideals $I, J$ are adjacent if and only if their intersection is nontrivial. In this paper, we investigate the connectedness of $Γ(S)$. We show that if $Γ(S)$ is connected then $diam(Γ(S)) \leq 2$. Further we classify the semigroups such that the diameter of their intersection graph is two. Other graph invariants, namely perfectness, planarity, girth, dominance number, clique number, independence number etc. are also discussed. Finally, if $S$ is union of $n$ minimal left ideals then we obtain the automorphism group of $Γ(S)$.
