论文标题
距离$ r $ - 域数和$ r $ - 独立的图形络合物
Distance $r$-domination number and $r$-independence complexes of graphs
论文作者
论文摘要
对于$ r \ geq 1 $，图$ g $的$ r $独立复合物，表示为ind $ _r（g）$，是一个简单的综合体，其面部为子集$ a \ subseteq v（g），因此诱导子级$ g [a] $的每个组件最多都有$ r $ $ $ Vertices。在本文中，我们建立了$ g $的距离$ r $ domination数量与ind $ _r（g）$的（同源）连接性之间的关系。我们还证明，对于和弦图$ g $，ind $ _r（g）$是可缩度或同质的，相当于球形的楔形。鉴于球体的楔形，我们还提供了弦弦图的结构，该图形图具有$ r $ ro $独立的综合体的同型楔形。
For $r\geq 1$, the $r$-independence complex of a graph $G$, denoted Ind$_r(G)$, is a simplicial complex whose faces are subsets $A \subseteq V(G)$ such that each component of the induced subgraph $G[A]$ has at most $r$ vertices. In this article, we establish a relation between the distance $r$-domination number of $G$ and (homological) connectivity of Ind$_r(G)$. We also prove that Ind$_r(G)$, for a chordal graph $G$, is either contractible or homotopy equivalent to a wedge of spheres. Given a wedge of spheres, we also provide a construction of a chordal graph whose $r$-independence complex has the homotopy type of the given wedge.
