论文标题
鉴于中央图的统治数，图形的新分类
New classification of graphs in view of the domination number of central graphs
论文作者
论文摘要
对于图$ g $，中央图$ c（g）$是从$ g $构建的图，它通过用一个顶点将$ g $的每个边缘细分，并通过为$ g $中的每对非贴上的顶点添加一个边缘。此外，对于图$ g $，让$γ（g）$和$τ（g）$是$ g $的统治数和$ g $的顶点盖的最低基数。在本文中，我们提供了有关中心图的支配数和图形最小顶点封面的新图表的新分类。也就是说，我们表明，任何具有至少三个顶点的图形$ g $都可以分为$γ（c（g））=τ（g）$和$γ（c（g））=τ（g）+1 $的两个类别之一，以及与$ g $的顶点覆盖物有关的一些特殊属性。我们还为中央图的主导数量提供了一些新的结果。
For a graph $G$, the central graph $C(G)$ is the graph constructed from $G$ by subdividing each edge of $G$ with one vertex and also by adding an edge to every pair of non-adjacent vertices in $G$. Also for a graph $G$, let $γ(G)$ and $τ(G)$ be the domination number of $G$ and the minimum cardinarity of a vertex cover of $G$, respectively. In this paper, we give a new classification of graphs concerning the domination number of central graphs and minimum vertex covers of graphs. Namely, we show that any graph $G$ with at least three vertices can be classified into one of the two classes of graphs with $γ(C(G))=τ(G)$ and $γ(C(G))=τ(G)+1$, respectively, together with some special properties concerning a vertex cover of $G$. We also give some new results on the domination number of central graphs.
