论文标题
在$ P_3 $ -HULL数字的$ Q $ -KNESER图形和Grassmann图
On the $ P_3 $-hull numbers of $ q $-Kneser graphs and Grassmann graphs
论文作者
论文摘要
令$ s $为有限字段$ \ mathbb {f} _q $上的$ n $维矢量空间，其中$ q $必然是主要功率。表示为\ emph {$ q $ -kneser graph}（$ k_q（n，k）$（resp。$ j_q（n，k）$），用于$ k \ geq 1 $的$ k \ geq 1 $，其顶点为$ k $ -dimensional $ s $ s $ s $ s $ v_1 $ \ dim（v_1 \ cap v_2）= 0 $（resp。$ \ dim（v_1 \ cap v_2）= k-1 $）。我们认为感染在$ Q $ -KNESER图和Grassmann图中扩散：如果至少有两个受感染的邻居，顶点会被感染。在本文中，我们分别计算$ p_3 $ -hull的$ k_q（n，k）$和$ j_q（n，k）$，这是最终感染整个图的顶点集的最小尺寸。
Let $S$ be an $n$-dimensional vector space over the finite field $\mathbb{F}_q$, where $q$ is necessarily a prime power. Denote $K_q(n,k)$ (resp. $J_q(n,k)$) to be the \emph{$q$-Kneser graph} (resp. \emph{Grassmann graph}) for $k\geq 1$ whose vertices are the $k$-dimensional subspaces of $S$ and two vertices $v_1$ and $v_2$ are adjacent if $\dim(v_1\cap v_2)=0$ (resp. $\dim(v_1\cap v_2)=k-1$). We consider the infection spreading in the $ q $-Kneser graphs and the Grassmann graphs: a vertex gets infected if it has at least two infected neighbors. In this paper, we compute the $ P_3 $-hull numbers of $K_q(n,k)$ and $J_q(n,k)$ respectively, which is the minimum size of a vertex set that eventually infects the whole graph.
