论文标题
发射率图中的无发生组和边缘支配
Incidence-free sets and edge domination in incidence graphs
论文作者
论文摘要
如果$ g $的每个边缘相交至少一个$γ$的边缘，而边缘支配数字$γ_e（g）$是边缘统治集的最小尺寸，则一组$ g $的边缘$γ$是一个边缘主导集。扩大了Laskar和Wallis的作品，我们研究了图$ G $的$γ_e（g）$，这是某些发病率结构$ d $的发病率图，重点是$ d $是一种对称的设计。特别是，在后一种情况下，确定$γ_e（g）$等同于确定某些无发生率的$ d $的最大尺寸。在整个过程中，我们采用了各种组合，概率和几何技术，并补充了光谱图理论的工具。
A set of edges $Γ$ of a graph $G$ is an edge dominating set if every edge of $G$ intersects at least one edge of $Γ$, and the edge domination number $γ_e(G)$ is the smallest size of an edge dominating set. Expanding on work of Laskar and Wallis, we study $γ_e(G)$ for graphs $G$ which are the incidence graph of some incidence structure $D$, with an emphasis on the case when $D$ is a symmetric design. In particular, we show in this latter case that determining $γ_e(G)$ is equivalent to determining the largest size of certain incidence-free sets of $D$. Throughout, we employ a variety of combinatorial, probabilistic and geometric techniques, supplemented with tools from spectral graph theory.
